Question

At a concert

Answer 1

Answer:

Each child ticket costs £2

Each adult ticket costs £5

Step-by-step explanation:

Let's define:

C = cost of a child ticket

A = cost of an adult ticket.

We know that:

"3 adult and 4 child tickets cost £23"

This can be written as:

3*A + 4*C = £23

"1 adult and 5 child tickets cost £15"

This can be written as:

1*A + 5*C = £15

Then we have the system of equations:

3*A + 4*C = £23

1*A + 5*C =  £15

To solve it, we start by isolating one of the variables in one of the equations:

Let's isolate A in the second equation:

A = £15 - 5*C

Now let's replace this in the first equation:

3*( £15 - 5*C) + 4*C = £23

Let's solve this for C

£45 - 15*C + 4*C = £23

£45 - 11*C =  £23

£45 - £23 = 11*C

£22 = 11*C

£22/11 = £2 = C

Each child ticket costs £2

And with the equation:

A = £15 - 5*C we can find the price of an adult ticket if we replace the value of C by £2

A = £15 - 5*£2 = £5

Each adult ticket costs £5