In Looking at Relationships Between Different Groups we discussed how to express and simplify ratios. Once you understand these concepts, you can use it to find unknown values in related ratios.

Remember we can write ratios as fractions to help us find unknown values in ratios.

Worked Example

Question 1

Consider the ratio $5:8$5:8.

If the following ratio is equivalent to $5:8$5:8, find the missing value.

$\editable{}$ : $32$32

If the following ratio is also equivalent to $5:8$5:8, find the missing value.

$400$400 : $\editable{}$

Applying ratios to everyday life

Ratios tell us about the relative sizes of two or more values. They are often used in everyday life, whether it's for dividing up money, betting odds, cooking or mixing cement! So knowing how to apply your knowledge about ratios is really important. Remember that the order that the words are written in the question correspond to the order of the values in the ratio so don't jumble them around.

Worked Examples

Question 2

A painter wants to create a certain colour by mixing two different colours of paint, Vespa and Nitro, in the ratio $6:1$6:1. He uses $3$3 litres of the Nitro colour.

How many litres of the Vespa colour must he use?

How many litres of paint will he have altogether once the two colours are combined?

Question 3

Tom and Jack divide their earnings of $£714$£714 in the ratio $10:7$10:7.

Find how much Tom receives.

Find how much Jack receives.

Question 4

There are two celebration dinners happening at Happy Mo's Restaurant. Each has $6$6 men at the table. At Beth’s birthday table there is a ratio of men to women of $1:3$1:3. At Buzz’s table the ratio is $3:1$3:1.

We want to find out what the ratio of men to women will be if the two celebration dinners join together.

What is the number of women at Beth's birthday table?

What is the number of women at Buzz's table?

What is the total number of men at the two tables?

What is the total number of women at the two tables?

Hence what is the ratio of men to women when the tables are combined?