math problem solving questions grade 10

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Problems with solutions and answers for grade 10.

Grade 10 math word problems with answers and solutions are presented.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

• An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.

Solutions to the Above Problems

• 6% x = 8,880 : x = selling price of house. x = $148,000 : solve for x.
• 3000 revolutions / minute = 3000×360 degrees / 60 seconds = 18,000 degrees / second
• L × W = 300 : area , L is the length and W is the width. 2 L + 2 W = 70 : perimeter L = 35 - w : solve for L (35 - W) × W = 300 : substitute in the area equation W = 15 and L = 20 : solve for W and find L using L = 35 - w.
• Let h be the height of the trapezoid. area = (1/2) × h × (10 + 10 + 3 + 4) = 270 h = 20 : solve for h 20 2 + 3 2 = L 2 : Pythagora's theorem applied to the right triangle on the left. L = sqrt(409) 20 2 + 4 2 = R 2 : Pythagora's theorem applied to the right triangle on the right. R = sqrt(416) perimeter = sqrt(409) + 10 + sqrt(416) + 17 = 27 + sqrt(409) + sqrt(416)
• 400 rev / minute = 400 × 60 rev / 60 minutes = 24,000 rev / hour 24,000 × C = 72,000 m : C is the circumference C = 3 meters
• Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat. 4x + 4y + 2z = 560 : 9x + 9y + 6z = 1,290 3x + 3y + 2z = 430 : divide all terms of equation C by 3 x + y = 130 : subtract equation D from equation B 3(x + y) + 2z = 430 : equation D with factored terms. 3*130 + 2z = 430 z = 20 : solve for z x + y + z = 130 + 20 = $150
• x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x
• Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system
• f(x) = -3(x - 10)(x - 4) = -3 x 2 + 42 x - 120 : expand and obtain a quadratic function h = -b/2a = - 42/(-6) = 7 : h is the value of x for which f has a maximum value f(h) = f(7) = 27 : maximum value of f.
• (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100) = (9/10)(10/11)(11/12)...(98/99)(99/100) = 9/100 : simplify
• Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B. d = 3(S + r) : boat travelling down river d = 5(S - r) : boat travelling up river 3(S + r) = 5(S - r) r = S / 4 : solve above equation for r d = 3(S + S/4) : substitute r by S/4 in equation B d / S = 3.75 hours = 3 hours and 45 minutes.
• Let: S be the speed of the airplane in still air, r be the speed of the wind and d the distance between A and B. d = 8(S - r) : airplane flies against the wind d = 7(S + r) : airplane flies in the same direction as the wind 8(S - r) = 7(S + r) S/r = 15

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Take Free State Assessment Practice Tests and Sample Questions for Grade 3 to 8 - Math & ELA

Sample Test Questions

Grade 10 math questions and solutions.

The Smarter Balanced Assessment Consortium (SBAC) is a standardized test that includes a variety of new technology-enhanced questions.

Some of them are Multiple choice-single correct responses, Multiple choice-multiple correct responses, Matching Tables, Drag and Drop, Hot text, Table Fill in, Graphing, Equation/numeric, Extended constructed response, Short answer, and many more.

This page contains several sample questions along with practice test links for Grade 10 Math that gives you an idea of questions that your students are likely to see on the test. After each sample question, an answer explanation follows. The explanation includes essential aspects of the task that you may need to consider for the skills, processes, and information your students need to know.

Domain: Grade 10 >> Number and Quantity – The Real Number System

Sample Question: Evaluate 9 150/300

Answer Explanation: 9 150/300 = 9 1/2 = square root of 9 = 3. In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. However, in this problem the exponent can be reduced, so we should reduce that first. The exponent 150/300 = 1/2. So the problem becomes 9 to the 1/2 power. The denominator is 2 so we take the square root of 9 which is 3. The numerator is 1 so we raise 3 to the 1st power and the answer is 3.

Standards: HSN.RN.A.1

Click here to practice: Number and Quantity – The Real Number System Questions on Grade 10 Math

Domain: Grade 10 >> Number and Quantity – Quantities

Sample Question: Rewrite x 1/2 in radical form.

Answer Explanation: In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. Since the problem is, x 1/2 , the denominator is 2 indicating we should take a square root and the numerator is 1 so we would raise that to the first power or there will be no exponent since an exponent of 1 is rarely used. That makes the answer the square root of x, written as √x.

Click here to practice: Grade 10 Number and Quantity – Quantities Questions

Domain: Grade 10 >> Number and Quantity – The Complex Number System

Sample Question: Simplify completely i(7−i)

Answer Explanation: i(7−i)=i*7−i*i=7i−i 2 =7i−(−1)=7i+1=1+7i

Start by using the distributive method. Now simplify −i 2 =1 by definition. Now rearrange and put the real part first and the imaginary part last so that it looks like this a+bi.

Standards: HSN.CN.A.2

Click here to practice: Grade 10 Math Number and Quantity – The Complex Number System Questions

Domain: Grade 10 >> Number and Quantity – Vector & Matrix Quantities

Sample Question: A vector in standard form has components . What is the initial point?

• Not enough information given

Answer Explanation: Since the vector is in standard position, we know that the initial point is (0, 0) or the origin.

Standards: HSN.VM.A.2

Click here to practice: Number and Quantity – Vector & Matrix Quantities Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Seeing Structure in Expressions

Sample Question: Which expression is equivalent to 9x 2 – 16y 2 ?

• (3x – 4y) (3x – 4y)
• (3x + 4y) (3x + 4y)
• (3x + 4y) (3x – 4y)
• (3x – 4y) 2

Answer Explanation: Student must recognize the expression is the difference of two perfect squares

Standards: HSA.SSE.A.2

Click here to practice: Algebra – Seeing Structure in Expressions Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Arithmetic with Polynomials & Rational Expressions

Sample Question: Evaluate f(x)=−a 3 +6a−7 at a = – 1 and state the remainder.

Answer Explanation: student must substitute – 1 into the function as follows −(−1) 3 +6(−1)−7=−12 and find the value to get the remainder

Standards: HSA.APR.B.2

Click here to practice: Algebra – Arithmetic with Polynomials & Rational Expressions Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Creating Equations

Sample Question: The ratio of staff to guests at the gala was 3 to 5. There were a total of 576 people in the ballroom. How many guests were at the gala?

Answer Explanation: Setup a proportion of guests to the total number of people, 8/5 = x/576. Solve by cross multiplying. 8x = 2880. Divide both sides by 8. So x=360.

Standards: HSA.CED.A.3

Click here to practice: Algebra – Creating Equations Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Reasoning with Equations & Inequalities

Sample Question: Solve the quadratic x 2 +10x=−25.

Answer Explanation: This problem can be easily solved by rearranging the equation so that it is solved for zero and then factoring as shown:

x 2 +10x=−25

x 2 +10x+25=0

(x+5)(x+5)=0

Since both factors are exactly the same, you will only have one solution to this problem.

Standards: HSA.REI.B.4

Click here to practice: Algebra – Reasoning with Equations & Inequalities Questions for Grade 10 Math

Domain: Grade 10 >> Functions – Interpreting Functions

Sample Question: Which graph could represent the graph of f(x)=sin(x)?

Answer Explanation: The sin function always graphs to look like a wave. The only one that could be the sin function is D.

Standards: HSF.IF.C.7

Click here to practice: Functions – Interpreting Functions Questions for Grade 10 Math

Domain: Grade 10 >> Functions – Building Functions

Sample Question: Describe how the graph of g(x)=x 3 – 5 can be obtained by shifting f(x) = x 3 + 2.

• Shift right 7 units
• Shift left 7 units
• Shift up 7 units
• Shift down 7 units

Answer Explanation: The only thing that changed in the two equations is the y-intercept which controls the vertical shift (up or down). To get the graph of g(x) by shifting the graph of f(x), you would shift f(x) down 7 units to change from +2 to -5.

Standards: HSF.BF.B.3

Click here to practice: Functions – Building Functions Questions for Grade 10 Math

Sample Question: Solve 3 x =12 using logarithmic form.

• x = ln12/ln3
• None of these

Answer Explanation: Solve using logs as follows 3 x =12 x=log(base 3) 12 x=ln12/ln3

Standards: HSF.LE.A.4

Domain: Grade 10 >> Functions – Trigonometric Functions

Sample Question: In the unit circle, one can see that tan(5π/4)=1 . What is the value of cos(5π/4)?

Standards: HSF.TF.A.2

Click here to practice: Functions – Trigonometric Functions Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Congruence

Sample Question: What would be the coordinates of point S after applying the following rule: (x+3, y -2)?

Answer Explanation: Answer: B Explanation: The transformation rule that is give is to translate the point 3 units to the right and 2 units down as shown by the following diagram:

Click here to practice: Geometry – Congruence Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Similarity, Right Triangles, & Trigonometry

Sample Question: By what property can the angles BAX and TSX be found to be congruent?

• Corresponding angles
• Vertical angles
• Alternate interior angles
• Congruent angles

Answer Explanation: Answer: A

Although they are congruent angles, the question is asking for the property. Since they are in corresponding locations with the transversal (AX) the correct answer is A

Standards: HSG.SRT.A.3

Click here to practice: Geometry – Similarity, Right Triangles, & Trigonometry Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Circles

Sample Question: What is the translation rule and the scale factor of the dilation as Circle F→Circle F′ ?

• (x,y)→1/4(x,y+10)
• (x,y)→4(x,y+10)
• (x,y)→1/4(x+10,y)
• (x,y)→1/4(x,y−10)

Answer Explanation: The original circle F has its center at the point (−5,−6) with a radius of 4 units. The translated/dilated circle F’ has its center at the point (−5,4) with a radius of 1 units. This means the center was translated up 10 units. As a transformation, this translation is written as (x,y)→(x,y+10). Circle F was also dilated by a factor of 1/4 because the radius was reduced from 4 units to 1 units. As a transformation, this dilation is written as (x,y)→1/4(x,y). Putting the translation and dilation together, the rule is (x,y)→1/4(x,y+10).

Click here to practice: Geometry – Circles Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Expressing Geometric Properties with Equations

Sample Question: What value on the number line in the figure below divides segment EF into two parts having a ratio of their lengths of 3:1?

Answer Explanation: Point E is at -7 on the number line in the figure, and pointF is at 1. Thus, the length of segment EF is 8. To divide the segment into two parts with a ratio of their lengths of 3:1, change the ratio to 3x:1x to allow variation in the location on the number line. Next, set the sum of the two parts equal to 8 and solve for x. 3x+1x=8;4x=8;x=2.Now, that you know that x=2, find 3x, which equals 6. Find the value on the number line by adding 6 to the position of point E. −7+6=−1.The value on the number line that divides segment EF in a ratio of 3:1 is -1.

Standards: HSG.GPE.B.6

Click here to practice: Geometry – Expressing Geometric Properties with Equations Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Geometric Measurement & Dimension

Sample Question: What is the volume of the prism shown below?

Answer Explanation: Use the formula for volume of a pyramid:

V=1/2.a.c.h

In this case the length is 15cm, the base is 10 cm in length, and the height is 9 cm. Therefore :

V=1/2.15.10.9=675cm 3

Standards: HSG.GMD.A.3

Click here to practice: Geometry – Geometric Measurement & Dimension Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Modeling with Geometry

Sample Question: A company ships spherical paperweights in cubic boxes. The circumference of the paperweight is 9π cm. If the box fits the sphere exactly with the sides of the sphere touching the box, what is the volume of the smallest box the company can use for shipping.

• 1009 π cm 3

Standards: HSG.MG.A.3

Click here to practice: Geometry – Modeling with Geometry Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Interpreting Categorical & Quantitative Data

Sample Question: Given the scatter plot below, what type of function expresses the correlation between the two variables?

• Exponential

Answer Explanation: Notice that the trend of the graph (in red) between the data points forms a line.

Standards: HSS.ID.A.4

Click here to practice: Statistics & Probability – Interpreting Categorical & Quantitative Data Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Making Inferences & Justifying Conclusions

Sample Question: In a research project about pet behavior, a random sample of 400 cats was chosen. The study showed that 60% of the cats preferred to sleep inside the house. Chicken was the favorite food for 35% of those cats. The study also showed that 85% of the cats that preferred to sleep outside the house had a different favorite dish. How many cats in the sample liked chicken the best and preferred to sleep inside?

Answer Explanation: If the sample has 400 cats and 60% of the cats preferred to sleep inside, then 400.0.60=240 cats preferred to sleep inside and 160 cats preferred to sleep outside. Next, if the favorite dish of 35% of those cats that preferred to sleep inside was chicken, then, 240.0.35=84 cats in the sample preferred to sleep inside and had chicken as their favorite dish.

Standards: HSS.IC.B.6

Click here to practice: Statistics & Probability – Making Inferences & Justifying Conclusions Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Conditional Probability & the Rules of Probability

Sample Question: A student council has one upcoming vacancy. The school is holding an election and has eight equally likely candidates. The AP Statistics class wants to simulate the results of the election, so the students have to choose an appropriate simulation method. They intend to do trials with the simulation. Which of these methods would be the most appropriate?

• Spin a wheel with eight equal spaces
• Toss a coin eight times for each election
• Throw a dice
• Throw four die

Answer Explanation: The question states that there are eight equally likely candidates. This means that each candidate has the same chance of winning the election. Only the spinning wheel with eight equal spaces could simulation this situation because the wheel has an equal chance of landing on each space.

Standards: HSS.IC.A.1

Click here to practice: Statistics & Probability – Conditional Probability & the Rules of Probability Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Using Probability to Make Decisions

Answer Explanation: Simply count the data points in circles C and E. There are 8 of them out of 24 total data points and by reducing we get 8/24=1/3.

Standards: HSS.CP.B.7

Click here to practice: Statistics & Probability – Using Probability to Make Decisions Questions for Grade 10 Math

Sample Question: A statistician is working for Sweet Shop USA and has been given the task to find out what the probability is that the fudge machine malfunctions messing up a whole batch of fudge in the process. Each malfunction of the machine costs the company $250. The statistician calculates the probability is 1 in 20 batches of fudge will be lost due to machine malfunction. What is the expected value of this loss for one month if the company produces 20 batches of fudge each day?

Answer Explanation: Since most months have 30 days we will assume 30 days in a month. We can use E(x)=x1p1+x2p2+…+xipi or simply calculate as follows E(X)=.05*250*30=$375

Standards: HSS.MD.A.4

Looking for online practice tests? Here is the link to practice more of SBAC Grade 10 Math questions.

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Jenny Watson

2 thoughts on “ grade 10 math questions and solutions ”.

Pingback: Create 10 questions for Grade 1 Algebra with explainations and answer choice - Parent.wiki

https://www.lumoslearning.com/llwp/sample-test-questions/sbac-sample-questions-grade-10-math.html

8/5 = x/576 should read 5/8 = x/576 The rest of the solution is correct so it’s a simple typo.

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Grade 10 Math Worksheets: FREE & Printable

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Tenth Grade (Grade 10) Problem Solving Strategies Questions

You can create printable tests and worksheets from these Grade 10 Problem Solving Strategies questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

• The cost of her other groceries.
• The number of mangoes she bought.
• The weight of each mango.
• The cost of each mango.
• 525,600 minutes
• 21,900 minutes
• 8,760 minutes
• 913 minutes
• Because this is dimensional analysis, regular rules of math do not apply.
• Since the necessary units cancel out, there is no problem.
• Because each of these factors is equal to one (the numerator and denominator are equal, but in different units).
• By the Multiplicative Property of Equality.
• One variable: C, the cost of moving.
• One variable: t, for the amount of time.
• Two variables: C, for the total cost, and t, for the amount of time.
• Two variables: t, for the amount of time, and d, for the distance traveled.
• One variable, the length of the side of the garden.
• One variables, the total perimeter of the garden.
• Two variables, the length and width of the garden.
• Two variables, the amount of fence he has, and the area of the garden.
• The rate of the water's increase, in liters per hour.
• The amount of water in the bucket, in liters.
• The amount of water in the bucket in liters and the amount of time that has passed in hours.
• The size of the bucket in liters and the rate of the drip in liters per hour.
• Yes, since [math]("N" * "m")/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"*"m"[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx 1/"kg" xx 1/"kg" xx "m"/1 = ("N" * "m"^3)/ ("kg"^4)[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx "m"/1 = "N" * "m"^3[/math].
• Yes, this is the correct model, and there are no more important factors to consider.
• No, this model leaves out many important variables, such as climate, water currents, diseases, and many more.
• No, only the current number of penguins and the historic rate of population growth are important. All the other factors are simply over-complicating the problem.
• Neither correct nor incorrect. Any real world problem can be modeled in multiple ways and with varying degrees of complexity.
• Hockey skill.
• Number of classes a student is taking.
• What type of movies he likes.
• Whether the student intends on attending university after he graduates high school.
• Number of calls placed to 9-1-1 from this neighborhood.
• When calls to 9-1-1 are placed from this neighborhood.
• Names of people arrested in this neighborhood.
• Criminal history of people arrested in this neighborhood.
• Yes, she is correct.
• No. She assumed that all terms need to have the same units, when all terms need to be without units.
• No. Although the variable [math]t[/math] is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
• No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to [math]"m"//"s"^2[/math] and the units of the last term are [math]"m"//"s"^4[/math].
• Just one variable, the average cost of a baked good.
• Two variables, one for the cost to make the baked goods, and another for the total revenue of the baked goods.
• Two variables, one for the total number of turnovers sold, and another for the total number of cupcakes sold.
• Two variables, one for the cost of a turnover, and one for the cost of a cupcake.
• [math]3 xx 778 xx 26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 1/26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 1/26.4 xx 1/2.5[/math]
• Amount of sunlight the plant will get.
• The size of the apartment.
• Whether she will put the plant on the floor or on a table.
• Average temperature of her apartment.
• The average number of tomatoes a tomato plant produces.
• The average weight of tomatoes a tomato plant produces.
• How long it takes to can one pound of tomatoes.
• The average weight of one can of tomatoes.
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Class 10 (Foundation)

Unit 1: basics, unit 2: number systems, unit 3: polynomials, unit 4: linear equations, unit 5: statistics, unit 6: probability, unit 7: mensuration, unit 8: coordinate geometry, unit 9: triangles, unit 10: quadrilaterals, unit 11: area of parallelograms and triangles, unit 12: circles.

GRADE  10 MATH QUESTIONS AND SOLUTIONS

Problem 1 :

Find greatest common factor of the following terms 

20x 3 , 36x 6

20  =  2 2  ⋅ 5

36  =  2 2  ⋅ 3 2

Greatest common factor  =   2 2  ⋅ 3 2  ⋅  5

  =  180

So, the g reatest common factor is  180 x 6 .

Problem 2 :

Simplify the following

p 2 - 1  =  (p+1) (p-1)

  =  [(p+1) (p-1)/p] ⋅ [p 3 /(p-1)]  ⋅ [1/(p+1)]

  =  p 2

Problem 3 :

Find the square root of 9801 by factor method.

So, the square root of 9801 is 99.

Problem 4 :

Solve 6x 2 + x - 1  =  0

6x 2  + x - 1  =  0

(3x - 1) (2x + 1)  =  0

So the solution is {-1/2, 1/3}.

Problem 5 :

The product of two consecutive odd number is 323. Find them.

Let x and x + 2 are two consecutive odd numbers. 

Product of two consecutive odd numbers =  323

x (x + 2)  =  323

x 2 + 2x  =  323

x 2  + 2x - 323  =  0

(x - 17)(x + 19)

x  =  17 and x  =  -19

So, the two odd numbers are 17 and 19.

Problem 6 :

Find two consecutive even integers whose product is 224.

Let x and x + 2 are two consecutive even integers.

Product of even integers  =  224

x(x + 2)  =  224

x 2 + 2x  =  224

x 2 + 2x - 224  =  0

(x + 16) (x - 14)  =  0

x  =  -16 and x  =  14

So, two consecutive even numbers are 14 and 16.

Problem 7 :

The length of the hall is 3 m more than its width. The numerical value of its area is equal to the numerical value of its perimeter. Find the length and width of the hall.

Let x be the width of the hall

length  =  x + 3

Area of the hall  =  Perimeter of the hall

x(x+3)  =  2(x+x+3)

x 2 + 3x  =  2(2x+3)

x 2  + 3x - 4x - 6  =  0

x 2  - 1x - 6  =  0

(x - 3)(x + 2)  =  0

x  =  3 and x  =  -2

x + 3  =  6

So, the width and length of the rectangle are 3 and 6 m.  

Problem 8 :

Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector approximately (use π = 3.14).

Area of major s ector  =  πr 2  - ( θ/360) πr 2

  =   π4 2  - (30 /360) π4 2

  =   π4 2 (1 - 1/12)

  =   π4 2 (11/12)

  =  (176/12)(3.14)

  =  46.05 cm 2

Problem 9 :

OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. 

Area of shaded region   =  Area of quadrant - Area of triangle ODB

  =   πr 2 - (1/2)  ⋅ base  ⋅ height

  =  (22/7)(3.5) 2  - (1/2)  ⋅ 3.5  ⋅ 2

  =  38.5 - 3.5

  =  35 cm 2

Problem 10 :

The wheels of a car are of diameter 80 cm each. Find how many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour.

Speed of the car  =  66 km/hr

 1000 m  =  1 km

  100 cm  =  1 m

66 km  =  6600000 cm

66 km/hr  =  6600000/60

  =  110000 cm/min

Distance covered  =  Time (Speed)

  =  10( 110000)

  =  1100000 

Radius of the wheel  =  40 cm

Number of revolutions

  =  Distance covered / Distance covered by 4 wheels

Distance covered by 4 whee l s  =  2 πr

  =  1100000 / [2 ( 3.14)  ⋅  40]

=  1100000/251.2

  =  4379

So, each wheel has to revolve 4379 times.

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There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
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