Greg is buying tickets for a fireworks display. There are three different ticket prices, adult, child and student. Greg’s friends have already bought tickets and paid the following:
Claire bought 5 adult tickets and 3 child tickets for a total of £85.00.
Helen bought 2 adult tickets, 1 child and 3 student tickets for a total of £58.00
Anthony bought 4 adult tickets and 2 child tickets for a total of £65.00
What is the total price for one adult ticket and one child ticket?
Answer:
Let:
A = price of adult ticket
C = price of child ticket
S = price of student ticket
5 A + 3 C = 85 (Eqn 1)
2 A + C + 3 S = 58 (Eqn 2)
4 A + 2 C = 65 (Eqn 3)
Equation 1 less equation 3 is equal to one adult and one child ticket ie:
5A + 3C – 4A – 2C = 85 -65
Therefore A + C = £20