Question

Ms. Diaz is thinking of buying an annual pass to Disneyland. The pass costs $109. Ms. Diaz must buy a funnel cake for $15 each time she visits the park. Write an expression for the daily cost if she buys an annual pass. Write an expression for the daily cost if she buys a daily pass. Use parts A and B to find how many days Ms. Diaz would have to go to make the annual pass less expensive than the daily.

A) Daily cost with annual pass = 109 + 15x, Daily cost with daily pass = 109 + 15
B) Daily cost with annual pass = 109 + 15, Daily cost with daily pass = 109 + 15x
C) Daily cost with annual pass = 15x, Daily cost with daily pass = 109 + 15
D) Daily cost with annual pass = 109 + 15x, Daily cost with daily pass = 109

Answer 1

The daily cost with an annual pass is (109/x) + 15 and for a daily pass, it's 109 + 15. To determine when the annual pass is a better deal, compare the cost of the annual pass for x days to the cost of x daily passes.

Step-by-step explanation:

The correct expression for the daily cost with an annual pass is the cost of the pass divided by the number of visits plus the cost of a funnel cake per visit. Therefore, if she visits x times, it will be (109/x) + 15. The expression for the daily cost if she buys a daily pass is just the cost of that single-day pass plus the cost of a funnel cake, which is 109 + 15. To find out how many days Ms. Diaz would have to go to the park to make the annual pass less expensive than the daily, you need to set the cost of the annual pass for x days (109 + 15x) less than or equal to the cost of x daily passes (x*(109 + 15)).

Solving the inequality 109 + 15x ≤ x(109 + 15), you will find the number of days needed for the annual pass to be the more economical option.