how to solve ratio story problems

Find here an unlimited supply of worksheets with simple word problems involving ratios, meant for 6th-8th grade math. In , the problems ask for a specific ratio (such as, " "). In , the problems are the same but the ratios are supposed to be simplified.

contains varied word problems, similar to these:

Options include choosing the number of problems, the amount of workspace, font size, a border around each problem, and more. The worksheets can be generated as PDF or html files.

Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:

Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

• Word Problems on Ratio

We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.

1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.

Let the previous weight be 5x.

x = \(\frac{65.7}{5}\)

Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.

2. Robin leaves $ 1245500 behind. According to his wish, the money is to be divided between his son and daughter in the ratio 3 : 2. Find the sum received by his son.

We know if a quantity x is divided in the ratio a : b then the two parts are \(\frac{ax}{a + b}\) and \(\frac{bx}{a + b}\).

Therefore, the sum received by his son = \(\frac{3}{3 + 2}\) × $ 1245500  

= \(\frac{3}{5}\) × $ 1245500

= 3 × $ 249100

= $ 747300  

3. Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers.

Let the numbers be 3x and 2x.

According to the problem,

\(\frac{3x + 2}{2x + 6}\) = \(\frac{4}{5}\)

⟹ 5(3x + 2) = 4

⟹ 15x + 10 = 8x + 24

⟹ 15x – 8x = 24 - 10

⟹ x = \(\frac{14}{7}\)

Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.

Thus, the numbers are 6 and 4.

4. If a quantity is divided in the ratio 5 : 7, the larger part is 84. Find the quantity.

Let the quantity be x.

Then the two parts will be \(\frac{5x}{5 + 7}\) and \(\frac{7x}{5 + 7}\).

Hence, the larger part is 84, we get

\(\frac{7x}{5 + 7}\) = 84

⟹ \(\frac{7x}{12}\) = 84

⟹ 7x = 84 × 12

⟹ 7x = 1008

⟹ x = \(\frac{1008}{7}\)

Therefore, the quantity is 144.

●  Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
• Dividing into a Given Ratio
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
• Problems on Ratio
• Worksheet on Ratio in Lowest Term
• Worksheet on Types of Ratios
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
• Worksheet on Dividing a Quantity in a Given Ratio
• Definition of Continued Proportion
• Mean and Third Proportional
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Word Problems: Ratios

When we solve word problems, we often encounter ratios. Whether we're aware of it or not, our universe contains many ratios -- including the so-called " golden ratio " that is so common in nature. When we understand how ratios work, it's easy to solve all kinds of real-world problems . Let's get started:

What is a ratio?

A ratio is a comparison of two different values with the same units. We write these with colons. Here are a few examples: 5:1, 12:30, 1:2

The colon simply means "to," so "5:1" means a "five to one" ratio.

Using our knowledge of ratios to solve word problems

Let's use our knowledge of ratios to tackle a few word problems:

Let's say we have 12 sunfish and 30 rainbow shiners in our backyard pond. What is the ratio of sunfish to rainbow shiners in its simplest form?

We can write the ratio 12:30 as the fraction 12 30 . Next, we can reduce this fraction to 2/5. Finally, we rewrite it as the ratio 2:5. We also know that the reverse is true, as the ratio of rainbow shiners to sunfish is 5:2.

Now let's say we have a classroom of 32 students with 20 girls. What is the ratio of boys to girls?

We know that the total is 32 -- but we can't make the mistake of giving 20/32 as our answer. This gives us the ratio of girls to the total number of students -- but it doesn't give us the ratio of girls to boys. To find the correct answer, we need the total number of boys.

30 - 18 = 12 boys

Therefore, the ratio of girls to boys is 20:12 or 5:3 in simplified terms.

Now let's say we're baking a cake using a recipe that calls for a butter-to-sugar ratio of 2:3. If we use 6 cups of butter, how many cups of sugar should we use?

We know that we're using three times as much butter as the original recipe (since 6 is three times 2), so all we need to do is multiply the original sugar amount by three as well.

3 × 3 = 9 cups of sugar.

So, if we use 6 cups of butter, we should use 9 cups of sugar to maintain the 2:3 butter-to-sugar ratio.

Topics related to the Word Problems: Ratios

Equivalent Ratios

Word Problems

Golden Ratio

Flashcards covering the Word Problems: Ratios

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Ratio Word Problems Calculator

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• The ratio of girls to boys is 5:4. There are 110 girls. How many boys are there?
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HOW TO SOLVE RATIO WORD PROBLEMS

In this section, you will learn how word problems on ratio can be solved.

Let us look at the stuff which are required to solve word problems on ratio. 

For example,

If two persons A & B are earning $400 and $ 500 respectively per week, the ratio of their earnings is 

A : B  =  400 : 500

When we simplify, we get  

A : B  =  4 : 5

From the ratio 4:5, if we want to get the earning of A and B, we have to multiply the terms of the ratio  4 & 5 by 100.

From the above point, it is very clear that if we want to get original quantity from the ratio, we have to multiply both the terms of the ratio by the same number.

In the above problem, we know that we have to multiply by 100. In case, we do not know what number to be multiplied, we have to multiply by "x" or any alphabet.

For example, the ages of two persons are in the ratio 

Age of the 1st person  =  5x

Age of the 2nd person  =  6x

(The value of 'x' to be found)

If a quantity increases or decreases in the ratio a : b,  then new quantity is

= 'b' of the original quantity divided by 'a' 

new quantity  =  (b x original quantity) / a

Increment Ratio :

In a ratio, if the second term is greater than the first term, it is called increment ratio.

Examples:  7 : 8 , 4 : 5, 1 : 5.

Decrement Ratio :

In a ratio, if the second term is smaller than the first term, it is called decrement ratio.

Examples : 8 : 7, 4 : 3, 9 : 7.

How to find increment ratio :

A quantity called 'A' has been increased to '3A'.

Now, to find the ratio in which it has been increased, just take the coefficient of A in the changed quantity '3A'. It is '3'.

Now we have to write this '3' as a fraction. That is 3/1. From the fraction '3/1', we have to form a increment ratio. Because, the original quantity has been increased. 

Therefore, the increment ratio from '3/1' is 1 : 3.

How to find decrement ratio :

A quantity called 'A' has been decreased to '0.25A'.

Now, to find the ratio in which it has been decreased, just take the coefficient of A in the changed quantity '0.25A'. It is '0.25'.

Now we have to write this '0.25' as a fraction. That is '1/4'. From the fraction '1/4', we have to form a decrement ratio. Because, the original quantity has been decreased. 

Therefore, the decrement ratio from '1/4' is 

Let us see how the above explained stuff help us to solve the ratio word problem given below.

Find in what ratio, will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

Let us understand the given information. There are two information given in the question. 

1. In a factory, there is a reduction in the number of workers in the ratio 15:11.

2. There is an increment in their wages in the ratio 22:25.

Target of the question :

In what ratio, will the total wages of the factory be increased or decreased ?

Let 'x' be the original number of workers 

Let 'y' be the wages per worker.

Total wages  =  (No. of workers) x (wages per worker)

Before the given two changes,

Total wages  =  xy  or  1xy

After reduction in the number of workers in the ratio

Number of workers in the factory is 

=  11x / 15   (see stuff 2)

After increment in wages in the ratio

Wages per worker is 

=  25y / 22   (see stuff 2)

After the two changes, 

Total wages  =  (11x/15) x (25y/22)

Total wages  =  (5/6)xy  =  (0.833)xy

Total wages  =  1xy  ----(1)

After the given two changes,

Total wages  =  (0.83)xy ----(2)

Comparing (1) and (2), it is very clear that total wages has been decreased when the two changes are applied.

That is, total wages has been decreased from  (1xy) to (0.83)xy

Now, to find the ratio in which it has been decreased, just take the coefficient of 'xy' in total wages after the two changes applied.

It is '0.83'.

Now we have to write this '0.83' as a fraction.

That is '5/6'.

From the fraction '5/6', we have to form a decrement ratio.

That is  '5 : 6' (See stuff 4).  

Therefore, the total wages of the factory will be decreased in the ratio

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Solving Word Problems with Ratios

Hey guys! Welcome to this video tutorial on word problems involving ratios .

Ratios are what we use to compare certain number values. People everywhere use ratios. We use, or at least we should, use ratios when we cook. For example, if I were to make macaroni and cheese for a group of 6 people and I knew that a \(\frac{1}{2}\) cup of macaroni would feed one person, then I could multiply 6 times \(\frac{1}{2}\) to get 3. Well, 3 to 6 is my ratio, and this ratio tells me that for every 3 cups of macaroni that I have, I can serve 6 people.

But hang on. What if I told you that 1 cup of macaroni to every 2 persons is the same ratio as 3:6? Well, it’s the same ratio. 3:6 can be reduced to 1:2 because both 3 and 6 are divisible by 3, which is how we get \(\frac{1}{2}\). So, even though these two ratios look different, they are actually the same.

Let’s take a look at a few word problems, and practice working through them.

Example Problem 1

There are 7 kids in a classroom with green shirts, 8 with red shirts, and 10 with yellow shirts. What is the ratio of people with red and yellow shirts? 7:10 8:7 8:10 4:5

Alright, so let’s look at our problem, and see what it is asking us to find, and write out the information that we have been given.

So, there are 7 kids with green shirts; so, let’s write that down. We have Green: 7. We have 8 kids with red shirts, so that is Red: 8, and we have 10 kids with yellow shirts, Yellow: 10.

So now let’s look at each of our options and eliminate. It can’t be 7:10, we don’t care about the green shirts. It can’t be 8:7, because again we don’t care about the green shirts. Option C is correct; that is the exact number ratio we found. Now, look closely at D here. Is 4:5 not the same thing as 8:10? 8 and 10 are both divisible by 2, and when we reduce them both down we get 4:5, so D is also correct!

Great, now let’s look at another word problem.

Example Problem 2

A vegetable tray contains 12 baby carrots, 27 cherry tomatoes, 18 florets of broccoli, and 45 slices of red bell peppers. For every 2 baby carrots, there are 3_____.

Alright, let’s start off the same way that we did our last problem; read through the problem, write down what we know, and find out what is being asked.

So, this vegetable tray contains 12 baby carrots. It contains 27 cherry tomatoes. We have 18 broccoli florets and 45 slices of red bell peppers.

When we look at all of our information written down, we can see that we have 18 broccoli florets; so there is our answer. For every 2 baby carrots, there are 3 broccoli florets.

Another way to check and verify that these two ratios are equal is by setting them up in fraction form and cross multiplying.

\(\frac{2}{3}=\frac{12}{18}\)

When we cross multiply, we get \(36=36\).

You can practice finding ratios anywhere you go, like finding the ratio of boys to girls in your class.

I hope that this video helped you to understand how to solve word problems with ratios.

See you guys next time!

Frequently Asked Questions

How do you figure out ratios.

A ratio is simply a comparison between two amounts. When figuring out ratios, it is important to consider what two values are being compared. This can be expressed in fraction form, in word form, or simply by using a colon.

When writing a ratio that is comparing a “part” to the “whole”, list the “part” first, and the “whole” second. For example, if you eat \(3\) slices of pizza out of \(10\) slices total, you have eaten \(3\) out of \(10\) slices. This can be expressed as \(\frac{3}{10}\) or \(3\):\(10\), where the part is listed first, and the whole is listed second.

Ratios can also be “part” to “part” comparisons. For example, if there are \(7\) boys in a class, and \(9\) girls in a class, the ratio of boys to girls is \(7\):\(9\). Make sure to match the order of the ratio to the order presented in the scenario.

What are basic ratios?

Ratios are used to directly compare two amounts. Basic ratios are used in many real-world situations, which makes it a valuable skill to master. Basic ratios can be expressed as fractions, words, or by using a colon. For example, \(\frac{4}{5}\), “four to five”, and \(4\):\(5\), all represent the same ratio.

What are the 3 ways to write a ratio?

A ratio is the comparison between two quantities. There is more than one way to write a ratio. For example, ratios can be written using a fraction bar, using a colon, or using words.

\(\frac{5}{8}\) \(5\):\(8\) \(\text{five to eight}\)

What are equivalent ratios?

Ratios that have the same value are considered equivalent ratios . For example, if you slice a cake into \(10\) pieces, and you eat \(2\) pieces, you have eaten “\(2\) out of \(10\)” pieces, or \(2\):\(10\). If you had sliced the cake into \(20\) pieces, and eaten \(4\) pieces, you would have eaten the same amount of cake. Eating “4 out of 20” pieces is the same amount as eating “2 out of 10” pieces. Equivalent ratios occur when you multiply or divide both quantities of the ratio by the same amount. \(\frac{50}{100}\) is equivalent to \(\frac{5}{10}\) because when you divide both quantities of the ratio by \(10\), the result is \(\frac{5}{10}\).

How do you find an equivalent ratio?

Equivalent ratios can be thought of as equivalent fractions. Two ratios are equivalent if they represent the same amount. For example \(\frac{1}{2}\) and \(\frac{5}{10}\) are equivalent because they represent the same amount. Equivalent ratios are found by multiplying or dividing the numerator and denominator by the same amount. For example, \(3\):\(4\) and \(15\):\(20\) are equivalent ratios because both values in \(3\):\(4\) can be multiplied by \(5\) in order to create the ratio \(15\):\(20\).

How do you solve ratio word problems?

Ratios have many real-world applications. Word problems that involve ratios will usually require you to find an unknown value by finding an equivalent ratio.

For example, if you made \($170\) washing \(10\) cars, how much money did you make per car? The ratio of dollars earned compared to cars washed is \(\frac{170}{10}\). We can divide both of these values by \(10\) in order to solve for the dollars earned for washing \(1\) car. \(\frac{170\div10}{10\div10}=\frac{17}{1}\). This means that \($17\) was earned per car. Many word problems involving ratios require you to create equivalent ratios. Remember, as long as you multiply or divide both values of a ratio by the same amount, you have not changed the ratio.

How do you write a ratio in words?

Ratios are used to compare two quantities. There are generally two ways to write a ratio in word form. When a ratio is considered a “part-out-of-whole” ratio, the phrase “out of” can be used. For example, if there is a pizza with \(8\) slices, and you eat \(2\) of those slices, you have eaten “\(2\) out of \(8\)” slices. However, some ratios are considered “part-to-part” ratios. For example, when comparing \(3\) green marbles to \(8\) red marbles, the phrase “\(3\) to \(8\)” can be used.

How do you explain ratios and proportions?

Ratios describe the relationship between two amounts. Ratios can be described as part-to-part or part-to-whole. For example, in a new litter of puppies, \(4\) of the pups are female and \(3\) of the pups are male. The part-to-part ratio \(4\):\(3\) would be used to compare female to male pups. When comparing female pups to the whole liter, the part-to-whole ratio \(4\):\(7\) would be used. Similarly, the ratio of male pups to total pups would be \(3\):\(7\). If two ratios are equivalent, they are said to be proportional. For example, if \(50\) meters of rope weighs \(5\) kilograms, and \(150\) meters of rope weighs \(15\) kilograms, the two amounts are proportional. \(50\):\(5\) is equivalent to \(150\):\(15\) because both values of the first ratio are multiplied by \(3\) in order to create the second ratio.

What is a ratio, short answer?

A ratio is a comparison between two amounts. Ratios can be written using a fraction bar \((\frac{3}{4})\), using a colon (\(3\):\(4\)), or using words (“three to four”). Ratios can be “part-to-part” or “part-to-whole”. For example, \(5\) green marbles and \(7\) red marbles would be a “part-to-part” ratio (\(5\):\(7\)). Solving \(95\) problems correctly out of \(100\) on a math test would be a “part-to-whole” ratio (\(95\):\(100\)).

Ratio Word Problems

  Cross multiply in order to determine which pair of ratios are equivalent.

3:5 and 4:9

6:7 and 7:8

7:8 and 35:40

12:25 and 14:17

The correct answer is 7:8 and 35:40. We can use cross multiplication to determine if two ratios are equivalent. Let’s look at the ratios for Choice C, and let’s set these up as fractions: \(\frac{7}{8}\) and \(\frac{35}{40}\)

Now, cross multiply by finding the product of \(8×35\) and \(7×40\). In both cases our product is 280, so we know that the original ratios are equivalent.

  Which ratio is equivalent to \(\frac{36}{45}\)?

The correct answer is 4:5. We can simplify ratios with the same strategy that we use to simplify fractions. In the ratio \(\frac{36}{45}\) we can divide the numerator and denominator by 9. \(\frac{36}{45}\) now becomes \(\frac{4}{5}\) or 4:5.

  James has a bag full of red, blue, and yellow candy. There are 10 red candies, 9 blue candies, and 11 yellow candies. What is the ratio of blue candies to total candies in the bag? Simplify the ratio if possible.

The correct answer is 3:10. The total number of blue candies is 9, and the total number of candies in the bag is 30. If we set this ratio up as a fraction, we have \(\frac{9}{30}\). This fraction can be simplified if we divide the numerator and denominator by 3. Our final answer is \(\frac{3}{10}\) or 3:10.

  Alex is counting the coins in his pocket, and finds that he has 14 quarters, 7 nickels, and 4 dimes. What is the ratio of quarters to nickels? Simplify if possible.

The correct answer is 2:1. We can compare the number of quarters to the number of nickels by setting up a ratio. There are 14 quarters and 7 nickels, so our ratio would be 14:7. Choice B says 14:7, but we should simplify when possible. 14:7 simplifies to 2:1.

  In Mr. Jenkin’s 4th grade class there are 14 boys and 17 girls. What is the ratio of boys to girls? Simplify if possible.

The correct answer is 14:17. We can express this comparison of boys to girls as a ratio. 14 boys and 17 girls can be described as the ratio 14:17, or the fraction \(\frac{14}{17}\). 14 and 17 do not have any factors in common, so 14:17 is in simplest form.

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by Mometrix Test Preparation | Last Updated: June 20, 2024

Ratio Word Problems - Two Terms Ratio

In these lessons, we will learn how to solve ratio word problems involving 2-term ratios.

Related Pages More Ratio Problems Math Word Problems Algebra Word Problems Math Worksheets

Ratio problems are word problems that use ratios to relate the different items in the question.

The main things to be aware about for ratio problems area:

• Change the quantities to the same unit if necessary.
• Write the items in the ratio as a fraction .
• Make sure that you have the same items in the numerator and denominator.

Ratio problems: Two-term Ratios

Example 1: In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution: Step 1: Assign variables: Let x = red sweets

Write the items in the ratio as a fraction.

Step 2: Solve the equation

Cross Multiply

3 × 120 = 4 × x 360 = 4 x

Isolate variable x

Answer: There are 90 red sweets.

Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution: Step 1: Sentence: Jane has 20 marbles, all of them either red or blue. Assign variables: Let x = blue marbles for Jane

20 – x = red marbles for Jane

We get the ratio from John John has 30 marbles, 18 of which are red and 12 of which are blue.

We use the same ratio for Jane.

3 × x = 2 × (20 – x ) 3 x = 40 – 2 x

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

Ratios and solving ratio word problems Examples:

• In a class there are 10 males and 15 females. What is the ratio of males to females?
• A classroom has a total of 30 students. There are 20 males. What is ratio of males to females?
• In a class the ratio of males to females is 4:5. If there are 36 total students, how many females are in the class?

How to use proportions to solve ratio word problems? Examples:

• The ratio of salamanders to frogs was 5 to 7. If there were 20 salamanders, how many frogs were there?
• If 3 sacks of concrete will make 12 square feet of sidewalk, predict how many sacks of concrete are needed to make 40 square feet of sidewalk.

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The Supreme Court says cities can punish people for sleeping in public places

Jennifer Ludden

U.S. Supreme Court says cities can punish people for sleeping in public places

A homeless person walks near an elementary school in Grants Pass, Ore., on March 23. The rural city became the unlikely face of the nation's homelessness crisis when it asked the U.S. Supreme Court to uphold its anti-camping laws. Jenny Kane/AP hide caption

In its biggest decision on homelessness in decades, the U.S. Supreme Court today ruled that cities can ban people from sleeping and camping in public places. The justices, in a 6-3 decision along ideological lines, overturned lower court rulings that deemed it cruel and unusual under the Eighth Amendment to punish people for sleeping outside if they had nowhere else to go.

Writing for the majority, Justice Gorsuch said, “Homelessness is complex. Its causes are many.” But he said federal judges do not have any “special competence” to decide how cities should deal with this.

“The Constitution’s Eighth Amendment serves many important functions, but it does not authorize federal judges to wrest those rights and responsibilities from the American people and in their place dictate this Nation’s homelessness policy,” he wrote.

In a dissent, Justice Sotomayor said the decision focused only on the needs of cities but not the most vulnerable. She said sleep is a biological necessity, but this decision leaves a homeless person with “an impossible choice — either stay awake or be arrested.”

The court's decision is a win not only for the small Oregon city of Grants Pass, which brought the case, but also for dozens of Western localities that had urged the high court to grant them more enforcement powers as they grapple with record high rates of homelessness. They said the lower court rulings had tied their hands in trying to keep public spaces open and safe for everyone.

Supreme Court appears to side with an Oregon city's crackdown on homelessness

But advocates for the unhoused say the decision won’t solve the bigger problem, and could make life much harder for the quarter of a million people living on streets, in parks and in their cars. “Where do people experiencing homelessness go if every community decides to punish them for their homelessness?” says Diane Yentel, president of the National Low Income Housing Coalition.

Today’s ruling only changes current law in the 9th Circuit Court of Appeals, which includes California and eight other Western states where the bulk of America’s unhoused population lives. But it will also determine whether similar policies elsewhere are permissible; and it will almost certainly influence homelessness policy in cities around the country.

Cities complained they were hamstrung in managing a public safety crisis

Grants Pass and other cities argued that lower court rulings fueled the spread of homeless encampments, endangering public health and safety. Those decisions did allow cities to restrict when and where people could sleep and even to shut down encampments – but they said cities first had to offer people adequate shelter.

That’s a challenge in many places that don’t have nearly enough shelter beds. In briefs filed by local officials, cities and town also expressed frustration that many unhoused people reject shelter when it is available; they may not want to go if a facility bans pets, for example, or prohibits drugs and alcohol.

Critics also said lower court rulings were ambiguous, making them unworkable in practice. Localities have faced dozens of lawsuits over the details of what’s allowed. And they argued that homelessness is a complex problem that requires balancing competing interests, something local officials are better equipped to do than the courts.

"We are trying to show there's respect for the public areas that we all need to have," Seattle City Attorney Ann Davison told NPR earlier this year. She wrote a legal brief on behalf of more than a dozen other cities. "We care for people, and we're engaging and being involved in the long-term solution for them."

The decision will not solve the larger problem of rising homelessness

Attorneys for homeless people in Grants Pass argued that the city’s regulations were so sweeping, they effectively made it illegal for someone without a home to exist. To discourage sleeping in public spaces, the city banned the use of stoves and sleeping bags, pillows or other bedding. But Grants Pass has no public shelter, only a Christian mission that imposes various restrictions and requires people to attend religious service.

"It's sort of the bare minimum in what a just society should expect, is that you're not going to punish someone for something they have no ability to control," said Ed Johnson of the Oregon Law Center, which represents those who sued the city.

He also said saddling people with fines and a criminal record makes it even harder for them to eventually get into housing.

Johnson and other advocates say today’s decision won’t change the core problem behind rising homelessness: a severe housing shortage, and rents that have become unaffordable for a record half of all tenants. The only real solution, they say, is to create lots more housing people can afford – and that will take years.

• homelessness
• Supreme Court

How much did debate hurt Biden's re-election bid? New poll offers insight.

Trump's new, narrow advantage signals a close contest, not a decisive lead. but other exclusive poll findings raise red flags for the president..

Republican Donald Trump has edged ahead of Democrat Joe Biden , 41% to 38%, in the aftermath of the candidates' rancorous debate last week , according to an exclusive USA TODAY/Suffolk University Poll.

That narrow advantage has opened since the previous survey in May showed the two contenders tied, 37% to 37% .

The findings still signal a close contest, not a decisive lead. The difference in support and the shifts since the spring are within the polls' margins of error of plus or minus 3.1 percentage points. The new survey of 1,000 registered voters was taken Friday through Sunday by landline and cell phone.

There was little change in the standing of third-party candidates, with independent Robert F. Kennedy Jr., at 8% and three others at about 1% each.

But other findings in the poll raised red flags for President Biden, whose campaign has been roiled by his faltering performance in the CNN debate last Thursday. In the survey, 41% of Democrats said they wanted Biden replaced at the top of the ticket.

"I think people are more focused on age, rather than with what the reality of our everyday could be under the two different administrations," said Shalia Murray, 57, a Democrat from Round Rock, Texas, who works in law enforcement and was called in the poll. She enthusiastically supports Biden but worries about voter apathy and a focus on "very surface issues."

"I don't believe a lot of people believe that we could actually go backwards in our rights and in our freedoms" in a Trump administration, she said.

Trump now leads as the second choice of voters: 25% of those surveyed said Trump was their second choice, compared with 17% for Biden. Thirty-three percent said their second choice was one of four third-party contenders: independent Cornel West, Green Party candidate Jill Stein, Libertarian candidate Chase Oliver and RFK Jr.

"It is still a margin of error race right now, but the Biden campaign must be concerned about the defection of second-choice votes of third-party voters," David Paleologos, director of the Suffolk Political Research Center, said. Some Democratic strategists had calculated those voters would drift back to Biden as Election Day neared.

"They now favor Trump instead of Biden," he said. "The Stein/West/RFK voters he may have been counting on in November have left him after Thursday's debate."

The enthusiasm gap could affect turnout

Trump voters are also much more excited about their candidate than Biden voters are about theirs. That enthusiasm gap could be critical when it comes to convincing supporters to actually cast a ballot in the fall.

"I like Trump," said Zach Anderson, 30, a maintenance technician and a Republican from South Chicago, Illinois. "The country was running just fine four or five years ago with him, and I can only see him doing a better job than he did last time because he has four years of experience."

In contrast, Steve Sutton, a political independent from Seattle who works in IT, said he is for Biden in part simply because he is against Trump.

In the debate, "Biden seems too old, and Trump can't tell the truth," he said. "So those are the two things coming out of it, and those are both, you know, right on the mark."

• By 2 to 1, 59% to 30%, Trump voters were more likely to say they were "very excited" about voting for their candidate.
• By 2 to 1, 37% to 16%, Biden voters were more likely to say they were "not very excited" or "not at all excited" about their candidate.

After years of sharpening political polarization, most partisans say their minds are firmly made up, including 87% of Biden voters and 89% of Trump voters. Just 10% of Biden supporters and 12% of Trump supporters say they might change their minds.

However, most of those backing third-party candidates said their minds might change, from 56% of Kennedy's backers to 80% of those supporting Stein.

Overall, 17% of those surveyed said they might change their minds.

More details: Joe Biden's core Democratic support takes big hit after debate, exclusive poll shows

For many, that would require a change in the nominees. In response to an open-ended question, 21% said "different candidates" and 16% said "a better candidate" would make them reconsider their choices.

There was skepticism about the power of the Republican national convention in July and the Democratic national convention in August to persuade. Fourteen percent said the two conventions might change their minds, and 12% said the Democratic convention might.

But a negligible 2% said the GOP convention might change their minds.

When it comes to congressional elections, 47% said they would vote for the unnamed Republican candidate in their district; 45% for the Democratic one. That edge, while small, could be encouraging for GOP hopes of retaining their narrow majority in the House of Representatives.

Trump supporters suspicious of the count

Trump's unsubstantiated allegations that the 2020 election was stolen from him have reinforced significant doubts among his supporters about whether they can trust the vote count this year.

In the poll, 44% of Trump supporters were "not confident" that the 2024 results would be accurately counted and reported, and another 45% said they were only "somewhat confident."

In contrast, 83% of Biden supporters were "very confident" in a fair count.

That said, Biden supporters were less certain they would prevail: 73% predicted a Biden victory, 12% a Trump win. Trump supporters were more bullish about November: 88% predicted Trump would win, just 4% Biden.

My husband died by suicide. How would I tell our young children?

The state trooper had delivered the news of Seth’s death. Soon, I was laser-focused on solving a single problem: How to tell the girls.

It was 10 years ago — July 1, 2014 — that everything changed.

A grim-faced state trooper pulled up to my house. I saw him from the living room window as he stepped out of the cruiser. He slammed the car door shut and took his time letting himself in through the wooden gate. He turned down the stone path. His slow, plodding footsteps gave him away. I flung open the front door and rushed down the steps toward him.

Part of me knew before I asked.

I remember the opposing compulsions tugging me in two at that moment: I want to know, I don’t want to know, like a child in a field, picking petals off a daisy. He loves me, he loves me not. I hesitated, just for a second, to speak. But the cop had a mission to complete. He was steady, stone-faced, with militaristic precision to his steps.

All morning, I’d been desperate for news of Seth, my husband, an MIT professor and father of our daughters, then 8 and 11. Here, finally, was the messenger. So often, the truth is nuanced, multifaceted, subjective, shaded gray. But this fact striding toward my doorstep was that rare, eminent type of truth: particular and inescapable.

“Is he dead?” I asked.

The cop’s response began with a gesture of his head. I saw it start to move, slowly, up and then down. As it did, mine began to shift too, rotating to the right, to the left and back, almost like we were locked in a dance, except that his motions finally stopped, while mine grew steadily faster, overwhelming my entire body, shaking off every moment that came before.

The cop nodded, “Yes.”

I fell to my knees, weeping, howling the only thoughts I could summon into words: “The girls, the girls, Oh God, the girls,” like an old vinyl record stuck in a scratched groove. The trooper took my arm. The world collapsed into a sickening, hyper-real haze. I floated above my body briefly, saw myself below like a Sicilian widow in a Coppola movie.

But I could not dissociate from the pain for my young daughters. Kneeling there, I felt I’d failed my key job as a mother, to protect them. As I tried to stand back up, my limbs, once solid, had now turned rubbery, unreliable. I leaned against the policeman as he led me back indoors, handing me over to a cousin who had arrived during my frantic morning search.

As we entered my living room, the state trooper cleared his throat uncomfortably. He asked if my daughters’ names were Sophia and Julia. I nodded. He looked straight at me: “There’s a note.” It was left on the dashboard of Seth’s car, abandoned on the Tobin Bridge from which he jumped.

I thought I’d vomit. “I don’t want it in here,” I said. “I can’t read it.” My cousin walked with the cop back to his car where she took the single sheet of paper.

She quickly folded it away, promising to keep it safe. Then she returned, placed her arms around my shoulders and begged me to breathe. In that instant all of the previous roles I’d embodied — wife, journalist, daughter — dissolved. The clarity of my new vocation as a ferocious watchdog mother infused my entire nervous system. I felt myself lapse into a kind of madness. My reality seemed impossible to inhabit. How do I tell my children, “Daddy died.” And, worse, how he died. They would never recover.

I sat on the couch, the last place I’d seen Seth that morning. My body was numb except for the dry matte of my tongue, thick and sour, like a bad piece of meat. Staring at the unfinished puzzle left on the floor, the one he’d worked on with the girls only hours earlier, I felt that language itself had betrayed me. Soothing words like “Marriage,” “Promise,” “Father” struck me now as poisonous, no longer bestowing the luxurious comforts that had tethered our lives. I had no backup to cling to, no map.

Yet I was fully aware of a deadline looming. The state trooper had delivered the news of Seth’s death shortly before noon. Within about an hour, I’d snapped into a mental state that was laser-focused on solving a single problem: How to tell the girls.

Now in my small office upstairs, I glanced at the old digital clock atop my wooden desk. It read 1:10 p.m. Day camp pickup was at three. How did a mother tell young children about their father’s death, I wondered. I desperately needed a script.

As a journalist, there was one thing I understood well: how to track down an expert for guidance. I dialed a trusted work colleague and explained that I required fast help finding the right words for Sophia and Julia. “I’m on it,” she said.

Ten minutes later, my colleague phoned back. I should stand by, she said. Then the phone rang again. Accustomed to speaking with strangers, I immediately blurted out my dilemma as soon as Dr. Paula Rauch, a psychiatrist from Massachusetts General Hospital, spoke her name.

“My husband is dead. My kids don’t know. What do I say?”

As I sat clutching my phone, Rauch calmly walked me through the language I might use to explain the unimaginable to my children.

I should speak plainly , she said.

I could tell them their daddy had an illness in his brain. We couldn’t see it, but just like cancer, it took over his body and made him die.

There was nothing any of us could have done. It was nobody’s fault.

Don’t lie, she advised, but don’t offer too many details.

I nodded throughout, saying little, taking notes.

Let them know they are safe and you’re not leaving, she said. Acknowledge their pain. Reassure them you will muddle through, things will get better.

Hanging up, I exhaled for what felt like the first time all day. I always appreciated a solid plan. This prescription, in the form of her words, offered me a lifeline.

When the time came, I drove the quarter mile from my house to the children’s camp and parked in the nearby lot. Thankfully, I wasn’t alone in the car. I knew it was best to speak to the kids on my own, but I was also becoming aware of a dynamic I’d largely avoided in parenting thus far: requiring help.

Before this moment, I had considered myself one of those older, therefore wiser, super-moms who could effortlessly go it alone. Now, I knew I wouldn’t be able to drive the girls home by myself after telling them. So, there in the car with me was my mother, who’d broken the speed limit all the way from Cape Cod to Cambridge that morning when I called her with the news. I’d also asked Maria, the children’s longtime babysitter, to join me for support.

They waited in the car as I stepped outside. I fixed my eyes on the girls as I walked hesitantly toward them. I felt the contrast between the burdensome weight of my knowledge and their easy, lighthearted ignorance. I pulled out my phone and snapped a photo of Julia, cross-legged on the ground, sitting in a circle of friends, giggling and clapping hands with the other children awaiting pickup. I wanted a record of what I believed would be her final carefree moment.

In a robotic stupor, my body adopted the persona I’d rehearsed over the past hours. I waved. They approached me. I led them to a wobbly chrome table outside Anna’s Taqueria, their favorite burrito place. I pulled both girls in close and told them I had very bad news.

“Girls, a terrible, terrible thing happened,” I said, holding their small hands. I paused. “Daddy died.” I couldn’t bear the silence that I expected would follow, so I began chattering to fill the space. “It was kind of an accident, but worse,” I said, grasping for phrasing that might offer some slight relief. “I don’t know all the details, there’s still a lot we don’t understand. But it’s true. And I am so, so sorry and I know it feels impossible now, but we will stay together and take care of each other and go on.”

The disbelief on their faces was so stark that I felt I had to repeat myself. “He’s dead.”

Sophia, who looks like Seth — with her tight, dark curls and deep set eyes — cried, “No!” and “How?”

Julia stood up on her chair: “I’m not even double digits yet,” she wailed.

When sundown finally arrived, someone, mercifully, brought me an Ativan. I tossed four extra pillows onto my bed. “We’re sleeping together,” I told the girls. It’s something we never repeated, despite my offers, because it triggered flashbacks of that day. While I held them, I replayed the nightmare morning in my head: the unanswered calls to Seth’s phone, the rising dread, the cop arriving, the note. Each memory, I believed, eroded any hope for an untroubled future.

With my children’s hot breath against my neck, and the time nearing 3 a.m., I tried to blot out these thoughts. Soon, we would have to endure another day. There would be decisions for me to make. I tried to yield toward a woozy, drugged half-sleep, still checking, with each passing hour, that their small chests continued to rise and fall.

Rachel Zimmerman is a journalist and writer based in Cambridge, Mass. who has previously written for The Washington Post and the Wall Street Journal. This is an excerpt from her book, “ Us, After: A Memoir of Love and Suicide ,” to be published June 30.

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