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Answer:
Difference = £10
Step-by-step explanation:
Represent adult with A and children with C
[tex]A + C = 28775[/tex]
[tex]C : A = 9 : 16[/tex]
[tex]Sales = 615785[/tex]
Required
Determine the difference in price of both tickets
[tex]A + C = 28775[/tex]
Convert ratio to fraction
[tex]C : A = 9 : 16[/tex]
[tex]\frac{C}{A} = \frac{9}{16}[/tex]
Cross Multiply
[tex]16C = 9A[/tex]
Make C the subject
[tex]C = \frac{9}{16}A[/tex]
Substitute [tex]C = \frac{9}{16}A[/tex] in [tex]A + C = 28775[/tex]
[tex]A + \frac{9}{16}A = 28775[/tex]
Take LCM
[tex]\frac{16A + 9A}{16} = 28775[/tex]
[tex]\frac{25A}{16} = 28775[/tex]
Multiply both sides by 16
[tex]16 * \frac{25A}{16} = 28775*16[/tex]
[tex]25A= 28775*16[/tex]
[tex]25A= 460400[/tex]
Make A the subject
[tex]A = \frac{460400}{25}[/tex]
[tex]A = 18416[/tex]
Substitute 18416 for A in [tex]C = \frac{9}{16}A[/tex]
[tex]C = \frac{9}{16} * 18416[/tex]
[tex]C = \frac{9* 18416}{16}[/tex]
[tex]C = \frac{165744}{16}[/tex]
[tex]C = 10359[/tex]
If a children ticket costs £15, then total children tickets cost:
[tex]Children = 10359 * 15[/tex]
[tex]Children = 155385[/tex]
The total sales is given as:
[tex]Sales = 615785[/tex]
So, the total cost of adult ticket is:
[tex]Adults = 615785 - 155385[/tex]
[tex]Adults = 460400[/tex]
Recall that number of adults is: 18416
So, an adult ticket costs
[tex]An\ adult\ ticket = \frac{460400}{18416 }[/tex]
[tex]An\ adult\ ticket = 25[/tex]
So, we have that:
Children Ticket = £15
Adult Ticket = £25
The difference is:
Difference = £25 - £15
Difference = £10