Question

A cinema sells adults tickets and child tickets.
The total cost of 3 adult tickets and 1 child tickets is £30
The total cost of 1 adult tickets and 3 child tickets is £22
Work out cost of an adult ticket and the cost of an child ticket?

Answer 1

Answer:

total cost of adult ticket is: £8.50

total cost of child ticket is: £4.50

STEP BY STEP EXPLANATION

Let the cost of adult ticket at the cinema be £x and the child ticket be £y.

The total cost of 3 adult tickets and 1 child ticket is £30

3x + y = 30

y = 30 - 3x…Eq..1

The total cost of 1 adult ticket and 3 child tickets is £22

x + 3y = 22

x = 22 - 3y…Eq..2

Substituting the value of x from Eq..2 to Eq. 1

y = 30 - 3x

y = 30 - 3 (22 - 3y)

y = 30 - 66 + 9y

y - 9y = - 36

—8y = —36

y = 36/8

y = £4.50

The child ticket is £4.50

Substituting the value of y in the Eq..2

x = 22 - 3y

x = 22 - 3 (4.50)

x = 22 - 13.50

x = £8.50

Adult ticket is £8.50

Answer the total cost of an adult ticket is £8.50 and the total cost of a child ticket is £4.50