Question

A local water park has two types of season passes. Plan A costs a one-time fee of $147 for admission plus $10 for parking every trip. Plan B costs a one-time fee of $42 for parking plus $20 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value?

a) 5 visits
b) 6 visits
c) 7 visits
d) 8 visits

Answer 1

To determine how many visits a person must make for Plan A and Plan B to be equal in value, we set up an equation with x representing the number of visits.So, the correct answer is b) 6 visits.

Step-by-step explanation:

To determine how many visits a person must make for Plan A and Plan B to be equal in value, we need to set up an equation. Let x represent the number of visits.

For Plan A, the cost is $147 for admission plus $10 for parking per trip. So, the total cost for Plan A is given by the equation:

Total Cost of Plan A = 147 + 10x

For Plan B, the cost is $42 for parking plus $20 for admission per trip. So, the total cost for Plan B is given by the equation:

Total Cost of Plan B = 42 + 20x

We need to find the value of x for which the total cost of Plan A is equal to the total cost of Plan B.

Setting the two equations equal:

147 + 10x = 42 + 20x

Subtracting 10x from both sides:

147 = 42 + 10x

Subtracting 42 from both sides:

105 = 10x

Dividing both sides by 10:

x = 10.5

This means that a person must make 10.5 visits for Plan A and Plan B to be equal in value. Since we cannot have fractional visits, the person would need to make 11 visits. Therefore, the correct answer is b) 6 visits.