SOLVING WORD PROBLEMS ON PROPORTION

Problem 1 :

Carter's SUV requires 8 gallons of gasoline to travel 148 miles. How many gasoline, to the nearest gallon, will he need for 500 mile trip?

Solution :

Let x be the quantity of gasoline in gallons.

8 : 148 = x : 500

Product of extremes = Product of means

8 ⋅ 500 = 148 ⋅ x

x = (8 ⋅ 500)/148

x = 27.02

So, Carter needs 27.02 gallons of gasoline for a 500 mile trip.

Problem 2 :

On a map 1 inch represents 5 miles. If a certain state is represented on a map by the rectangle 10 inches by 7.2 inches. What is the area of the state in square miles ?

Solution :

length of rectangle = x and width of the rectangle = y

Area of rectangle = 50(36)

= 1800 square miles

Problem 3 :

Together there are 754 students and teachers in the meeting. If the ratio of students to teachers is 27 : 2, how many teachers are there ?

Solution :

Total number of students and teachers = 754

number of students =  27x

number of teachers = 2x

27x + 2x = 754

29x = 754

x = 754/29

x = 26

Problem 4 :

Concrete is made by mixing cement, sand and gravel in the ratio 5 : 9 : 13. How much cement is needed to make 324 ft³ of concrete?

Solution :

Quantity of cement, sand and gravel is 5x, 9x and 13x respectively.

5x + 9x + 13x = 324

27x = 324

x = 324/27

x = 12

Quantity of cement = 5x = 5(12) = 60

Required quantity of cement is 60 ft³.

Problem 5 :

If Andy drove 84 miles in 1 hour 45 minutes, how many miles can he drive in 5 hours?

Solution :

1 hour 45 minutes :

45 minutes = 45/60 hours = 3/4 hours 

1 hour 45 minutes = 1¾ hours

Let x be the number of miles.

84 : 1¾ = x : 5

84 : 7/4 = x : 5

84 ⋅ 5 = 7/4 ⋅ x

x = 420 (4/7)

x = 1680/7

x = 240

Number of miles he can drive is 5 hours is 240 miles.

Problem 6 :

A collection of quarters, dimes and nickels is worth $5. If the ratio quarters to dimes to nickels is 2 : 4 : 7, how many quarters are there?

Solution :

$5 = 500 cents

1 quarter = 0.25 cents

1 dime = 0.1 cents

1 nickel = 0.05 cents

Let number of quarters, dimes and nickels be 2x, 4x and 7x.

2x(0.25) + 4x(0.1) + 7x(0.05) = 5

0.5x + 0.4x + 0.35x = 5

1.25x = 5

x = 5/1.25

x = 4

Number of quarters = 2(4) = 8 quarters.

Problem 7 :

If 5x/3 = (x + 14)/2, what is the value of x?

Solution :

5x/3 = (x + 14)/2

By doing cross multiplication, we get

10x = 3(x + 14)

10x = 3x + 42

7x = 42

x = 42/7

x = 6

Problem 8 :

A trail mix contains raisin, peanut, and chocolate. The ratio of raisin to peanut is 2:3 and the ratio of peanut to chocolate is 5:8. What is the ratio of raisin to chocolate?

Solution :

Ratio of raisin to peanut is 2 : 3.

Ratio of peanut to chocolate is 5 : 8.

By finding compound ratio, we get

2 : 3 = 10 : 15

5 : 8 = 15 : 24

10 : 15 : 24

Ratio between raisin and chocolate = 10 : 24.

= 5 : 12

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