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

The cost of an adult ticket is £11 and the cost of a child ticket is £8.50.

Step-by-step explanation:

To find the cost of an adult ticket and a child ticket, we need to set up a system of equations. Let's say the cost of an adult ticket is 'a' and the cost of a child ticket is 'c'.

From the given information, we can set up the first equation as: 3a + 4c = 67 .

The second equation can be set up as: 5a + 6c = 106 (Jones family).

Now, we can solve these equations simultaneously to find the values of 'a' and 'c'.

Multiplying the first equation by 5 and the second equation by 3 will give us:

15a + 20c = 335,

15a + 18c = 318.

Subtracting the second equation from the first, we get:

2c = 17. Therefore, c = 17/2 = 8.5.

Substituting the value of 'c' back into the first equation, we can find the value of 'a'.

3a + 4(8.5) = 67.

3a + 34 = 67.

3a = 67 - 34.

3a = 33.

a = 33/3 = 11.

So, the cost of an adult ticket is £11 and the cost of a child ticket is £8.50.