Question

One hundred and fifty tickets were sold for a basketball match and $560 was the total amount collected. Adult tickets were sold at $4 each and child tickets were sold at $1.50 each. How many tickets and how many child tickets were sold?

Answer 1

`134` adult tickets and
`16` child tickets were sold.

Explanation:

Let
`a` represents the number of adult tickets sold and
`c` represents the number of child tickets.

The total number of tickets sold was
`150`. So we can write the equation,

`a+c=150...eqn(1)`

Adult tickets were sold at $
`4` each. This means that,
`a` number of adult tickets will yield $
`4a`.

Child tickets were sold at $
`1.50` each. This means that,
`c` number of adult tickets will yield $
`1.50c`.

The total amount collected was $
`560`.

We can write this equation for the total amount collected.

`4a+1.50c=560...eqn(2)`

Let us make
`a` the subject in equation (1) to get,

`a=150-c...eqn(3)`

We put equation (3) in to equation (2) to get,

`4(150-c)+1.50c=560`

We expand the brackets to get,

`600-4c+1.50c=560`

We group like terms to get,

`-4c+1.50c=560-600`

`-2.5c=-40`

We divide both sides by
`-2.5` to get,

`c=(-40)/(-2.5)`

This implies that,

`c=16`

We substitute
`c=16` into equation (3) to get,

`a=150-16`

`\Rightarrow a=134`

Hence
`134` adult tickets and
`16` child tickets were sold.