Question

two types of memberships are available for a water park:

• an unlimited use membership for $70 per month, or
• a monthly $10 fee plus $5.00 per visit.

enter an equation that can be used to find the number of visits (v) per month needed for the two membership types
to cost the same amount.

Explanation:

Step1: <Cost of unlimited use membership>

The cost of the unlimited - use membership is a fixed amount. Let \(C_1\) be the cost of the unlimited - use membership. So, \(C_1 = 70\).

Step2: <Cost of the other membership>

Let \(v\) be the number of visits. The cost of the second membership (\(C_2\)) has a fixed part (\(10\)) and a variable part (\(5v\)). So, \(C_2=10 + 5v\).

Step3: <Set the two costs equal>

We want to find when \(C_1 = C_2\). So, we set up the equation \(70=10 + 5v\).

Answer:

\(70 = 10+5v\)