Question

The local zoo has two options for membership: basic and VIP. The basic membership is $146 for the year. With the basic membership, it costs $30 every time you park your car to visit. The VIP membership is $389 for the year. However, the cost for parking is only $5 each time with the VIP membership. How many times visiting and parking would it take for the memberships to cost the same amount for the year?

Answer 1

The cost of the basic and VIP zoo memberships will be the same after 10 visits, when accounting for the differing parking fees associated with each membership level.

Step-by-step explanation:

To determine how many times visiting and parking at the zoo would cause the cost of the basic and VIP memberships to be the same, we need to set up an equation where the cost of both memberships is equal. Let's denote the number of visits as 'n'.

For the basic membership, the total cost with parking is:
Cost = Basic Membership Fee + (Parking Fee per Visit × Number of Visits)
Cost = $146 + ($30 × n)

For the VIP membership, the total cost is:
Cost = VIP Membership Fee + (Parking Fee per Visit × Number of Visits)
Cost = $389 + ($5 × n)

To find the number of visits required for both memberships to cost the same, we solve the equation:
$146 + ($30 × n) = $389 + ($5 × n)

Subtract $146 and $5n from both sides to get:
$30n - $5n = $389 - $146
$25n = $243

Now, divide both sides by $25 to find 'n':
n = $243 / $25
n = 9.72

Since you can't visit the zoo a fraction of a time, it would take 10 visits for the VIP membership to match the total cost of the basic membership and parking.