Question

The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.

Answer 1

Part (a)

The variable y is the dependent variable and the variable x is the independent variable.

Part (b)

The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:

$0.75\times 18=13.5$ dollars

Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.

Therefore, the price of the fair admission is: $33.50-$13.50=$20

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be  written as:

$y=0.75x+20$......Equation 1

Part (c)

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.