Question

There are some people in a cinema.

3/5 of the people in the cinema are children
For the children in the cinema,
Number of girls:number of boys = 2:7
Their are 170 girls in the cinema
Work out the number of adults

Answer 1

`Adults = 510`

Explanation:

Given

`Children = (3)/(5)`

`Girls:Boys = 2 : 7`

`Girls = 170`

Required

Determine the number of adults

First, we need to calculate the number of children

`Girls:Boys = 2 : 7`

Given that:
`Girls = 170`

Substitute 170 for Girls in
`Girls:Boys = 2 : 7`

`170 : Boys = 2 : 7`

Convert to fraction

`(170)/(Boys) = (2)/(7)`

Cross Multiply

`Boys * 2 = 170 * 7`

Divide both sides by 2

`Boys = (170 * 7)/(2)`

`Boys = (1190)/(2)`

`Boys = 595`

So, the number of children are:

`Children = Boys + Girls`

`Children = 595 + 170`

`Children = 765`

Next, we calculate the number of people in the cinema.

`Children = (3)/(5) * People`

Substitute 765 for Children

`765 = (3)/(5) * People`

Make People the subject.

`People = (765 * 5)/(3)`

`People = (3825)/(3)`

`People = 1275`

If 3/5 are children, then 2/5 are adults.

So:

`Adults = (2)/(5) * 1275`

`Adults = (2* 1275)/(5)`

`Adults = (2550)/(5)`

`Adults = 510`