Identifying Statements that Describe a Ratio

We should remember that certain words or phrases, such as ‘in’, ‘per’, ‘for every’, ‘out of’, and ‘to’, indicate ratios. We look for such words or phrases in word problems on ratios and reduce the statements to ratio notation and solve them accordingly.

For every 5 boys on a softball team there is 1 girl. What is the ratio of boys to girls?

Solution

Step 1:

Here the words we look for to indicate a ratio are ‘for every’.

Step 2:

The given statement means there are 5 boys to 1 girl or the ratio of boys to girls is 5 to 1 or 5:1

At the carnival, for every 8 games, there are 9 rides. Find the ratio of rides to games.

Solution

Step 1:

Here the words we look for to indicate a ratio are ‘for every’.

Step 2:

The given statement means there are 9 rides to 8 games or the ratio of rides to games is 9 to 8 or 9:8.

The cost of apples is $1.23 per apple. What is the ratio of dollars to apples?

Solution

Step 1:

The word we look for to indicate a ratio is ‘per’.

Step 2:

The statement means that each apple costs $1.18. The ratio of dollars to apples is $1.18 to 1 apple or 1.18:1; $frac{1.18}{1}$

Out of 5 children, 3 are girls. What is the ratio of girls to children?

Solution

Step 1:

The words we look for to indicate a ratio here are ‘out of’.

Step 2:

The statement means that the ratio of girls to children is 3:5.

1 in 3 persons is single. what is the ratio of single persons to all people?

Solution

Step 1:

The word we look for to indicate a ratio is ‘in’.

Step 2:

The given statement means that the ratio of single persons to all people is 1:3.