Question

Two families go to a theatre.
The Smith family of three adults and four children pay £67.
The Jones family of five adults and six children pay £106.
Work out the cost of an adult ticket and the cost of a child ticket.​

Answer 1

SOLUTION

GIVEN

• Two families go to a theatre.

• The Smith family of 3 adults and 4 children pay £67.

• The Jones family of 5 adults and 6 children pay £106.

TO DETERMINE

The cost of an adult ticket and a child ticket.

EVALUATION

Let the cost of an adult ticket = £ x and the cost of a child ticket = £ y

Now it is given that the Smith family of 3 adults and 4 children pay £ 67.

∴ 3x + 4y = 67 - - - - - - (1)

Again the Jones family of 5 adults and 6 children pay £106

∴ 5x + 6y = 106 - - - - - - (2)

2 × Equation 2 - 3 × Equation 1 gives

10x - 9x = 212 - 201

∴ x = 11

From Equation 1 we get

$\sf{(3 \times 11) + 4y = 67}$

$\sf{ \implies \: 33 + 4y = 67}$

$\sf{ \implies \: 4y = 34}$

$\sf{ \implies \: y = 8.5}$

Hence the cost of an adult ticket = £ 11 and the cost of a child ticket = £ 8.5

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