Stuck on problem need help solving

Question

A local water park has two types of season passes. Plan A costs a one-time fee of $144 for admission plus $10 for parking every trip. Plan B costs a one-time fee of $48 for parking plus $22 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value ?

Answer 1

Hi Avery,

A local water park has two types of season passes. Plan A costs a one-time fee of $144 for admission plus $10 for parking every trip. Plan B costs a one-time fee of $48 for parking plus $22 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value ?

Given: Plan A Cost = $144 one time plus $10 parking per trip

Plan B Costs = $48 one time plus $22 each trip.

Find: The number of visits when the plan cost is equal.

Let v = number of visits.

Cost A = $144 + $10 v

Cost B = $48 + 22 v

Find when costA = Cost B

144 + 10 v = 48 + 22v

96=12v

v = 8

So after 8 visits the cost should be equal.

You can check by determining the cost of a and b

Cost A = $144 + $10 v

Cost A = $144 + 10 (8) = 144+80 = 224

Cost B = $48 + 22 v

Cost B = $48 + 22 (8) = 48 + 176 = 224

It checks out