Question

Mr and Mrs Smith buy tickets for hemselves and their four children.

The cost of an adult ticket is £ 6 more than the cost of a child ticket .The total cost of the 6 tickets is 40.50 .
Work out the cost of an adult ticket.
In your working let c be the cost of a child ticket and a be the cost of an adult ticket.

Answer 1

Cost of an adult ticket is £10.75

Explanation:

Given:-

Cost of 1 adult ticket is £6 more that the cost of a child ticket.

Total cost of 6 tickets = £40.50

c is cost of a child ticket and a is the cost of an adult ticket.

To find:- Cost of 1 adult ticket =?

Solution:-

For 2 adults and 4 children, and the total cost of tickets is £40.5, we get the following equation,

`2a+4c=40.5` -----------------(1)

As the Cost of 1 adult ticket is £6 more than the cost of a child ticket, we can the following equation,

`a=c+6` -----------------(2)

Now, substituting the value of a from equation 2 in equation 1 we get,

`2a+4c=40.5`

`2(c+6)+4c=40.5`

`2c+12+4c=40.5`

`6c=40.5-12`

`6c=28.5`

`c=(28.5)/(6)`

`c=4.75` --------------------(3)

Now substituting the value of c from equation 3 in equation 2,

`a=c+6`

`a=4.75+6`

`a=10.75`

As a is the cost of 1 adult ticket,

Therefore Cost of an adult ticket is £10.75