The Zoo has an adult price and a child price for their tickets.
A group of 4 adults and 5 children paid a total of £136.00.
A group of 3 adults and 2 children paid a total of £81.00.
Work out the price for one adult ticket and the price for one child ticket.
Answer:
Let a be the price of an adult ticker and c be the price of a child ticket
4a + 5c = 136
3a + 2c = 81
Then multiply the first equation by 3 and the second equation by 4
12a + 15c = 408
12a + 8c = 324
Therefore, since the total price of the adult tickets is constant in the new equations the change in price must be from the child tickets so the increase in price between the first and second equation is equal to the price of the difference between the number of children tickets in the new equations
Therefore,
7c = 84
c = £12
Therefore, by substituting this price of £12 into the first equation you get
4a = 76
a = £19
The price of one adult ticket is £19.00 and the price for one child ticket is £12.00.