Question

28775 tickets are sold for a football match. Children’s tickets cost £15. The ratio of children to adults is 9:16.

If the total ticket sales makes £615785, what is the difference between the price of an adults ticket and a children’s ticket?

Answer 1

Difference = £10

Explanation:

Represent adult with A and children with C

`A + C = 28775`

`C : A = 9 : 16`

`Sales = 615785`

Required

Determine the difference in price of both tickets

`A + C = 28775`

Convert ratio to fraction

`C : A = 9 : 16`

`(C)/(A) = (9)/(16)`

Cross Multiply

`16C = 9A`

Make C the subject

`C = (9)/(16)A`

Substitute
`C = (9)/(16)A` in
`A + C = 28775`

`A + (9)/(16)A = 28775`

Take LCM

`(16A + 9A)/(16) = 28775`

`(25A)/(16) = 28775`

Multiply both sides by 16

`16 * (25A)/(16) = 28775*16`

`25A= 28775*16`

`25A= 460400`

Make A the subject

`A = (460400)/(25)`

`A = 18416`

Substitute 18416 for A in
`C = (9)/(16)A`

`C = (9)/(16) * 18416`

`C = (9* 18416)/(16)`

`C = (165744)/(16)`

`C = 10359`

If a children ticket costs £15, then total children tickets cost:

`Children = 10359 * 15`

`Children = 155385`

The total sales is given as:

`Sales = 615785`

So, the total cost of adult ticket is:

`Adults = 615785 - 155385`

`Adults = 460400`

Recall that number of adults is: 18416

So, an adult ticket costs

`An\ adult\ ticket = (460400)/(18416 )`

`An\ adult\ ticket = 25`

So, we have that:

Children Ticket = £15

Adult Ticket = £25

The difference is:

Difference = £25 - £15

Difference = £10