Question

The owners of the amusement park introduce a Family Ticket. This allows two adults to have one go on each of four different rides and for two children to have one go on each of the six different rides and for the children to have an extra go on their favourite ride. The owners will set the price for a Family Ticket so that, whatever rides the family chooses to use it for, it would not have been cheaper to buy the tokens. (c) What is the maximum price that could be set for the Family Ticket?

Answer 1

The maximum price that could be set for the Family Ticket is $11X.

Step-by-step explanation:

To find the maximum price that could be set for the Family Ticket, we need to compare the cost of buying tokens for each individual ride with the cost of the Family Ticket.

Let's assume that the price of a token is $X and the price of the Family Ticket is $Y.

The family consists of two adults and two children. The adults will have one go on each of four different rides, so their total cost would be 4 times the price of a token, which is 4X.

The children will have one go on each of six different rides, plus an extra go on their favorite ride. This means they will have a total of 7 rides. Since the children are entitled to an extra go on their favorite ride, the total cost for the children would be 7 times the price of a token, which is 7X.

Therefore, the cost of buying tokens for the family would be 4X + 7X = 11X.

Thus, the maximum price that could be set for the Family Ticket is $11X, as long as it is higher than the cost of buying tokens for all the rides.