# Proportions Word Problems Worksheet

Proportions Word Problems Worksheet
• Page 1
1.
Justin takes 3.2 hours to draw a painting. Estimate the number of such paintings that he can draw in 12 hours.
 a. 5 b. 3 c. 6 d. 4

#### Solution:

Time taken to draw one painting = 3.2 hours 3 hours
[Round to the nearest whole number.]

Let n be the number of paintings Justin can draw in 12 hours.

Number of paintings he can draw in 3 hoursTime taken = Number of paintings he can draw in 12 hoursTime taken

1 / 3 = n / 12
[Write a proportion.]

3 × n = 1 × 12
[Write the cross products.]

n = 1 × 123
[Divide by 3 on both sides.]

n = 4
[Simplify.]

So, Justin can draw about 4 paintings in 12 hours.

2.
There are 60 eggs for every 5 trays in a shop. Find the ratio of the number of eggs to the number of trays.
 a. 12 to 1 b. 5 to 6 c. 1 to 12 d. 6 to 5

#### Solution:

eggstrays = 605

= 60 ÷ 55 ÷ 5
[Divide both numerator and denominator by their GCF 5.]

= 121

So, the ratio of the number of eggs to trays is 12 : 1.

3.
The height of a eucalyptus tree in a park is 12 feet. It casts a shadow of 6 feet. A maple tree in the same park casts a shadow of 2 feet. Find the height of the maple tree.
 a. 16 feet b. 8 feet c. 24 feet d. 4 feet

#### Solution:

Let x be the height of the maple tree.

x2 = 126
[Write a proportion.]

6x = 12 × 2
[Write the cross products.]

6x6 = 12×26
[Divide both sides by 6.]

x = 4
[Simplify.]

The height of the maple tree is 4 feet.

4.
Victor was standing beside a lamppost. He noticed that the lamppost is casting a shadow of about 11.6 feet long and his own shadow was about 2.9 feet long. Find the approximate height of Victor, if the height of the lamppost was 23.2 feet.
 a. 7.8 feet b. 5.8 feet c. 4.8 feet d. 6.8 feet

#### Solution:

Let x be the height of Victor.

11.62.9 = 23.2x
[Write a proportion.]

11.6x = 2.9 × 23.2
[Write the cross products.]

11.6x11.6 = (2.9×23.2)11.6
[Divide both sides by 11.6.]

x = 5.8
[Simplify.]

Therefore, the height of Victor is 5.8.

5.
Andrew bought 8 shirts for $520. How much would he need to pay for 10 shirts at the same rate?  a.$650 b. $715 c.$416 d. \$520

#### Solution:

x = 14
[Simplify.]

6.
Ed observed that a man 6 feet tall casts a shadow of 4 feet. At the same time, the shadow cast by a building is 24 feet. What is the height of the building?
 a. 36 feet b. 96 feet c. 16 feet d. 26 feet

#### Solution:

height of the man length of his shadow= height of the buildinglength of its shadow
[The triangles formed with their respective shadows are similar.]

64 = x24
[Substitute the values. x is the height of the building.]

4 × x = 6 × 24
[Write the cross products.]

4x4 = (6×24)4
[Divide both sides by 4.]

x = 36
[Simplify.]

So, the height of the building is 36 feet.

7.
Tony wants to draw a picture of Diana Hayden by seeing her photograph. The actual length and width of the photograph are 1 foot and $\frac{1}{2}$ foot respectively. If the length of the picture he wants to draw is 2 feet, then find the width of the picture.
 a. 5 feet b. 1 foot c. 3 feet d. 2 feet

8.
A museum displayed a model of a fighter plane. The length of the model is 29 cm and the scale used to make the model was 1 cm to represent 1.2 ft. What would be the actual length of the plane?
 a. 24.17 ft b. 30.2 ft c. 34.8 ft d. 31.2 ft

#### Solution:

Let n be the actual length of the plane.

1 / 1.2 = 29n
[Write the scale and its related proportion.]

n × 1 = 1.2 × 29
[Write the cross products.]

n = 34.8
[Simplify.]

The actual length of the plane is 34.8 ft.

9.
Jim has drawn a picture of the Eiffel Tower using a scale 1 inch : 82 $y$$d$ as shown. Find the actual height of the Eiffel Tower.

 a. 328 $y$$d$ b. 322 $y$$d$ c. 326 $y$$d$ d. 324 $y$$d$

#### Solution:

Let n be the height of the actual Eiffel Tower.

182 = 4n
[Write the scale and its related proportion.]

n × 1 = 82 × 4
[Write the cross products.]

n = 328
[Multiply.]

The actual height of the Eiffel Tower is 328 yd.

10.
The architect, who designed the plan for hospital building was told that the height of the hospital building should not exceed 247 feet. The architect designed the building on paper using a scale 2 inch : 19 feet. What should be the height of the building on paper?
 a. 27 in. b. 25 in. c. 28 in. d. 26 in.

#### Solution:

Let n be the height of the building on paper.

219 = n247
[Write the scale and its related proportion.]

n x 19 = 247 x 2
[Write the cross products.]

n = 26
[Divide both sides by 19 and then simplify.]

The height of the building on paper is 26 in..