Over half term two families went to a food and drink festival.
Family A is made up of 5 adults and 4 children and paid a total of £78.00 for their tickets.
Family B is made up of 3 adults and 6 children and paid a total of £63.00 for their tickets.
Assuming each adult paid the same price and each child paid the same price.
Find the total price for one adult ticket and one child ticket.
Answer:
Family A:
5A + 4C = 78 (equation 1)
Equation 1 x 3:
15A + 12C = 234 (equation 2)
Family B:
3A + 6C = 63 (equation 3)
Equation 3 x 2
6A + 12C = 126 (equation 4)
Equation 2 – Equation 4:
15A – 6A + 12C – 12C = 234 – 126
9A = 108
A = 12
Substituting back into equation 1:
5 x 12 + 4C = 78
4C =78 -60
4C = 18
C = 4.50
Total price of one adult and one child ticket = 12 + 4.50 = £16.50
Answer: Adult £12.00 / Child £4:50