HOW TO SOLVE RATIO WORD PROBLEMS

Problem 1 :

If x : 15 = 10 : 3, find the value of x.

Solution:

So, the value of x is 50.

Problem 2 :

If the ratio of the populations of Africa and Europe is 5 : 4, find the population of Africa if Europe's population is 728 million.

Solution:

Let Africa population be x.

5 : 4 = x : 728

So, population of Africa is 910 million.

Problem 3 :

The ratio of the average population density per km² of Asia to that of Australia is 60 : 1. If the average in Asia is 152 people per km², what is the average in Australia?

Solution:

Let average in Australia be x.

60 : 1 = 152 : x

So, the average in Australia is 2.5 people per km².

Problem 4 :

The ratio of the population of Sydney to the population of Melbourne is 7 : 6. If 4.2 million people live in Sydney, how many people live in Melbourne?

Solution:

Let people live Melbourne be x.

7 : 6 = 4.2 : x

So, 3.6 million people live in Melbourne.

Problem 5 :

If 84 jellybeans are divided between Naomi and Luke in the ratio 4 : 3, how many jellybeans does each receive?

Solution:

Total jellybeans = 84

Ratio = 4 : 3

4x = Number of jelly beans received by Naomi

3x = Number of jelly beans received by Luke.

4x + 3x = 84

7x = 84

x = 12

Naomi = 4x = 4(12)

= 48

Luke = 3x = 3(12)

= 36

So, Naomi gets 48 jellybeans and Luke gets 36 jellybeans.

Problem 6 :

The sizes of the angles of a triangle are in the ratio 2 : 3 : 4. Find the size of each angle.

Solution:

The angles of a triangle are in the ratio 2 : 3 : 4.

Let the angles be 2x, 3x, 4x

The sum of angles of a triangle = 180°

2x + 3x + 4x = 180°

9x = 180°

x = 20°

So, 2x = 2(20) = 40°

3x = 3(20) = 60°

4x = 4(20) = 80°

Hence, the size of each angles are 40°, 60° and 80°.

Problem 7 :

A total of 22 million people live in the cities of Tokyo and Moscow. If the ratio of the populations of Tokyo and Moscow is 6 : 5. What is the population of each city?

Solution:

Total people = 22 million

Population of Tokyo = 6x

Population of Moscow = 5x

6x + 5x = 22 

11x = 22 

x = 2 

Tokyo population = 6x = 6(2)

= 12 million

Moscow population = 5x = 5(2)

= 10 million

Problem 8 :

At Christ Church, Cobargo, in 1914, there were 60 baptisms. The ratio of males to females who were baptised was 3 : 2. How many of each were baptised?

Solution:

Let males be 3x and females be 2x.

3x + 2x = 60

5x = 60

x = 12

Number of Male = 3x = 3(12)

= 36

Number of Female = 2x = 2(12)

= 24 

So, 36 males and 24 females.