WORD PROBLEMS ON PROPORTIONS

Definition of proportion :

Proportion is an equation that defines that the two given ratios are equivalent to each other.

In other words, the proportion states the equality of the two fractions or the ratios.

Proportions are denoted by the symbol '::' or '='.

In proportion,

The two ratios are a : b & c : d. 

Cross Product Rule :

Product of extremes  =  Product of means

ad  =  bc

Problem 1 :

A car travels 120 miles in 3 hours (with a constant speed). How far will it take to travel 200 miles?

Solution :

The ratio between distance traveled and number of hours is

120 : 3 -----> (1)

Let 'x' be the number of hours for 200 miles.

Then,

200 : x ----->(2)

From (1) and (2), we get

120 : 3 = 200 : x

120/3 = 200/x

By cross multiply,

120(x) = 200(3)

120(x) = 600

Divide each side by 120.

x = 600/120

x = 5 

It takes to travel 5 hours for 200 miles.

Problem 2 :

50 apples cost $25. How much would 75 apples cost? 

Solution :

The ratio between the number of apples and the cost is 

50 : 25 ----->(1)

Let ‘x’ be the cost of 75 apples.

Then,

75 : x ----->(2)

From (1) and (2), we get

50 : 25 = 75 : x

50(x) = 75(25)

50x = 1875

Divide each side by 50.

x = 1875/50

x = 37.5

So, the cost of 75 apples is $37.5.

Problem 3 :

It takes Mike18 minutes to finish reading 4 pages of a book. How long does it take for him to finish reading 30 pages?

Solution :

The ratio between the number of minutes and number of pages to finish reading a book is

18 : 4 ----->(1)

Let ‘x’ be the number of minutes to read 30 pages.

Then,

x : 30 ----->(2)

From (1) and (2), we get

18 : 4 = x : 30

18(30) = x(4)

540 = 4x

Divide each side by 4.

540/4 = x

x = 135

It takes 135 minutes to read 30 pages.

Problem 4 :

Nathan packs 25 boxes in 2 hours. How many boxes can he pack in his 8 – hour shift?

Solution :

The ratio between number of boxes and time taken

= 25 : 2 ----->(1)

Let ‘x’ be the number of boxes pack in 8 hours.

Then, 

= x : 8 ----->(2)

From (1) and (2), we get

25 : 2 = x : 8

25(8) = x(2)

200 = 2x

Divide each side by 2.

200/2 = x

x = 100

So, Nathan packs 100 boxes in 8 hours.

Problem 5 :

13 candy bars weigh 26 ounces. What is the weight of 35 candy bars?

Solution :

The ratio between the number of candy bars and the weigh of ounces is

13 : 26 -----> (1)

Let ‘x’ be the weight of 35 candy bars.

Then,

35 : x ----->(2)

From (1) and (2), we get

13 : 26 = 35 : x

13(x) = 35(26)

13x = 910

Divide each side by 13.

x = 910/13 

x = 70

So, the weight of 35 candy bars is 70 ounces.

Problem 6 :

A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine produce in 1 hour?

Solution :

The ratio between the number of yards of fabric and time taken is 

6 : 2 -----> (1)

Let ‘x’ be the number of yards of fabric in 1 hour.

Then,

1 hour = 60 minutes

x : 60 -----> (2)

From (1) and (2) we get

6 : 2 = x : 60

6/2 = x/60

6(60) = x(2)

360 = 2x

Divide each side by 2.

360/2 = x

180 = x

So, the machine can produce 180 yards of fabric in 1 hour.

Problem 7 :

24 loaves of bread cost $48. How much does 10 loaves cost?

Solution :

The ratio between the number of loaves and the bread cost is 

24 : 48 ---->(1)

Let ‘x’ be the cost of 10 loaves.

Then,

10 : x -----> (2)

From (1) and (2),

24 : 48 = 10 : x

24/48 = 10/x

24(x) = 10(48)

24x = 480

Divide each side by 24.

x = 480/24

x = 20

So, the cost of 10 loaves is $20.