Applying Proportional Relationships-Gr 8-Solved Examples

Solved Examples and Worksheet for Applying Proportional Relationships

Q1The ratio of boys to girls in a school is 5 : 4. Find the number of girls, if the number of boys in the school is 350.
A. 290
B. 280
C. 270
D. 320

Solutions

Step: 1

Let n be the total number of girls in the school.

Step: 2

54 = 350n

[Write a proportion in terms of Number of boysNumber of girls.]

Step: 3

5 × n = 4 × 350

[Write the cross products.]

Step: 4

5n = 1400

[Multiply.]

Step: 5

5n5 = 14005

[Divide both sides by 5.]

Step: 6

n = 280

Step: 7

The total number of girls in the school is 280.

Correct Answer is : 280

Q2One kilometer (km) is equal to 0.62 miles (mi) approximately. The flying distance between City - A and City - B is about 1550 mi. What is this distance in kilometers?
A. 2500 km
B. 2501.2 km
C. 2498.7 km
D. 961.0 km

Solutions

Step: 1

Let d be the distance in kilometers.

Step: 2

0.621 = 1550d

[Write proportion in mileskilometers.]

Step: 3

0.62 × d = 1 × 1550

[Write cross products.]

Step: 4

0.62d = 1550

[Multiply.]

Step: 5

0.62d0.62 = 15500.62

[Divide both sides by 0.62.]

Step: 6

d = 2500

Step: 7

The flying distance between City - A and City - B is 2500 km.

Correct Answer is : 2500 km

Q3It takes the Concorde 3.75 hours to fly a distance of 3,630 mi from New York to Paris. How long would it take the Concorde to circle the Earth?(Hint: The diameter of the earth is around 25168 miles)
A. 2600 hours
B. 24 hours
C. 968 hours
D. 26 hours

Solutions

Step: 1

Let n be the number of hours the Concorde takes to circle the Earth.

Step: 2

36303.75 = 25168n

[Write a proportion.]

Step: 3

3630 x n = 25168 x 3.75

[Write the cross products.]

Step: 4

3630n = 94380

[Multiply.]

Step: 5

3630n3630 = 943803630

[Divide both sides by 3630.]

Step: 6

n = 26

Step: 7

The Concorde would take 26 hours to circle the Earth.

Correct Answer is : 26 hours

Q4Henry has two milk cans which can hold milk in the ratio of 4 : 5. Find the capacity of the smaller can, if the capacity of the larger can is 25 gallons.

A. 25 gallons
B. 16 gallons
C. 20 gallons
D. 24 gallons

Solutions

Step: 1

Let n be the capacity of the smaller can (in gallons).

Step: 2

45 = n25

[Write a proportion.]

Step: 3

4 × 25 = 5 × n

[Write the cross products.]

Step: 4

100 = 5n

[Multiply.]

Step: 5

1005 = 5n5

[Divide both sides by 5.]

Step: 6

20 = n

[Simplify.]

Step: 7

The capacity of the smaller can is 20 gallons.

Correct Answer is : 20 gallons

Q5A hare says to a tortoise, "I can cover ten times the distance that you can travel in same time." The tortoise proudly replies, "I can cover one mile in just 5 hours." How far can the hare go in one hour?
A. 1 mi
B. 8 mi
C. 2 mi
D. 7 mi

Solutions

Step: 1

The distance covered by the tortoise in one hour = 15 = 0.2 mi.

[Since Distance = SpeedTime.]

Step: 2

Let n be the number of miles that hare can cover in one hour.

Step: 3

101 = n0.2

[Write a proportion.]

Step: 4

10 × 0.2 = 1 × n

[Write the cross products.]

Step: 5

2 = n

[Multiply.]

Step: 6

Hare can cover 2 mi in one hour.

Correct Answer is : 2 mi

Q6A mechanic finds that the ratio of mileages of a car and a bike is in the ratio of 1 : 3. Find the average mileage of the bike, if the average mileage of the car is 11 mi/L.

A. 22 mi/L
B. 34 mi/L
C. 44 mi/L
D. 33 mi/L

Solutions

Step: 1

Let h be the average fuel mileage of bike (in mi/L).

Step: 2

13 = 11h

[Write a proportion.]

Step: 3

1 × h = 3 × 11

[Write the cross products.]

Step: 4

h = 33

[Simplify.]

Step: 5

The average mileage of bike is 33 mi/L.

Correct Answer is : 33 mi/L

Q7You lose 0.08 lb of body fat if you walk for an hour. How long should you walk to lose 3 lb of body fat?
A. 38.5 hours
B. 47.5 hours
C. 37.5 hours
D. 41.5 hours

Solutions

Step: 1

Let t be the number of hours of walk required to lose 1 lb of weight.

Step: 2

0.083 = 1t

[Write a proportion.]

Step: 3

0.08 × t = 3 × 1

[Write the cross products.]

Step: 4

0.08t = 3

[Multiply.]

Step: 5

0.08t0.08 = 30.08

[Divide each side by 0.08.]

Step: 6

t = 37.5

[Simplify.]

Step: 7

You should walk about 37.5 hours to lose 3 lb of weight.

Correct Answer is : 37.5 hours

Q8Five centimeters is equivalent to two inches. The measure of the foot size of Danielle is 312 inches. Write the size of her foot in centimeters.

A. 17
B. 8.75
C. 10.25
D. 11.25

Solutions

Step: 1

Let n be the measure of foot size of Danielle in centimeters.

Step: 2

23.5 = 5n

[Write a proportion.]

Step: 3

2 × n = 5 × 3.5

[Write the cross products.]

Step: 4

2n = 17.5

[Multiply.]

Step: 5

2n2 = 17.52

[Divide both sides by 2.]

Step: 6

n = 8.75

Step: 7

The size of Danielle's foot is 8.75 cm.

Correct Answer is : 8.75

Q9A model of the solar system is displayed in a planetarium. A sphere with diameter 7 ft represents the Sun. The diameter of the Sun is 109 times the diameter of the Earth. Estimate the diameter of the model represented as the Earth.

A. 1.1 ft
B. 0.7 in.
C. 0.7 ft
D. 1.2 in.

Solutions

Step: 1

Let n be the diameter of the model represented as the Earth (in inches).

Step: 2

7 feet = 7 × 12 = 84 in.

[Convert feet into inches.]

Step: 3

1091 = 84n

[Write a proportion.]

Step: 4

109 × n = 84 × 1

[Write the cross products.]

Step: 5

109n = 84

[Multiply.]

Step: 6

109n109 = 84109

[Divide both sides by 109.]

Step: 7

n ≈ 0.7

Step: 8

Therefore the diameter of the model represented as the Earth is about 0.7 in.

Correct Answer is : 0.7 in.

Q10Lactometer is the instrument used to measure the purity of milk. Mr. Tony uses a lactometer and finds that milk and water are mixed in the ratio of 4 : 3. How many liters of water is mixed with 16 liters of milk?
A. 16 liters
B. 13 liters
C. 12 liters
D. 14 liters

Solutions

Step: 1

Let n be the number of liters of water.

Step: 2

43 = 16n

[Write a proportion in terms of milk/water.]

Step: 3

4 × n = 3 × 16

[Write the cross products.]

Step: 4

4n = 48

[Multiply.]

Step: 5

4n4 = 484

[Divide both sides by 4.]

Step: 6

n = 12

Step: 7

12 liters of water was mixed with 16 liters of milk.

Correct Answer is : 12 liters

Q11A snowball of radius 6 in. is rolling down from the top of a mountain. It is observed that for every 10 ft that the snowball travels, its radius increases by 1 in. Find the radius of the snowball after it travels 40 ft.

A. 9 in.
B. 12 in.
C. 10 in.
D. 11 in.

Solutions

Step: 1

Let r be the increase in radius of the snowball (in inches).

Step: 2

101 = 40r

[Write the proportion in terms of feet/inches.]

Step: 3

10 × r = 1 × 40

[Write the cross products.]

Step: 4

10r = 40

[Multiply.]

Step: 5

10r10 = 4010

[Divide both sides by 10.]

Step: 6

r = 4

Step: 7

The radius increases by 4 in.

Step: 8

The final radius of the snowball = Initial radius + Increase in radius = 6 + 4 = 10 in.

Step: 9

So, the radius of the snowball after it travels 40 ft is 10 in.

Correct Answer is : 10 in.

Q12An object weighing 120 lb on Earth would weigh only 20 lb on Moon. How much would Emily (48 lb on Earth) weigh on Moon?

A. 28 lb
B. 18 lb
C. 38 lb
D. 8 lb

Solutions

Step: 1

Let n be the weight of Emily on moon (in lb).

Step: 2

12020 = 48n

[Write a proportion in terms of Weight on EarthWeight on Moon.]

Step: 3

120 × n = 20 × 48

[Write the cross products.]

Step: 4

120n = 960

[Multiply.]

Step: 5

120n120 = 960120

[Divide both sides by 120.]

Step: 6

n = 8

Step: 7

Emily would weigh 8 lb on Moon.

Correct Answer is : 8 lb

Q13Nathan consumes 4 liters of water per day. In how many days will he consume 36 liters of water?
A. 11
B. 9
C. 10
D. 8

Solutions

Step: 1

Let y be the number of days Nathan takes to consume 36 liters of water.

Step: 2

4y = 36

[Write the linear equation.]

Step: 3

4y4 = 364

[Divide each side by 4.]

Step: 4

y = 9

[Simplify.]

Step: 5

Nathan takes 9 days to consume 36 liters of water.

Correct Answer is : 9

Q14A hare says to a tortoise, "I can cover 3 times the distance that you can travel in same time." The tortoise proudly replies, "I can cover one mile in just 2 hours." How far can the hare go in one hour?
A. 6 mi
B. 0.5 mi
C. 1.5 mi
D. 1 mi

Solutions

Step: 1

The distance covered by the tortoise in one hour = 12 = 0.5 mi.

[Since Distance = SpeedTime.]

Step: 2

Let n be the number of miles that hare can cover in one hour.

Step: 3

31 = n0.5

[Write a proportion.]

Step: 4

3 × 0.5 = 1 × n

[Write the cross products.]

Step: 5

1.5 = n

[Multiply.]

Step: 6

Hare can cover 1.5 mi in one hour.

Correct Answer is : 1.5 mi

Q15A map is drawn to a scale, such that a distance of 1 inch on the map represents a distance of 80 miles. What is the distance between the two cities, Rupert and Rushville, if the distance between them is 6.3 inches on the map?
A. 504 miles
B. 560 miles
C. 400 miles
D. 480 miles

Solutions

Step: 1

Let m be the distance between the two cities (in miles).

Step: 2

180 = 6.3m

[Write a proportion.]

Step: 3

1 × m = 80 × 6.3

[Write the cross products.]

Step: 4

m = 504

[Multiply.]

Step: 5

The distance between Rupert and Rushville is 504 miles.

Correct Answer is : 504 miles

Solved Examples and Worksheet for Applying Proportional Relationships

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HighSchool Math