Answer:
Each child ticket costs £2
Each adult ticket costs £5
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