Question

A local aquatic center and gym has two pay plans for community members to choose from. The preferred plan costs $1.50 per visit and has a one time fee of $300. The basic plan costs $5 per visit with a one time fee of $25. The preferred plan definitely costs more in the beginning, but at some point, it appears the basic plan will cost more than the preferred plan. After how many visits will the preferred plan and the basic plan cost the same?

A) 50 visits
B) 60 visits
C) 70 visits
D) 80 visits

Answer 1

The number of visits when the preferred plan and basic plan will cost the same is 79 visits.

Step-by-step explanation:

To find the number of visits when the preferred plan and basic plan will cost the same, we need to set up an equation.

Let's assume that after x number of visits, the cost of the preferred plan and the basic plan will be equal.

For the preferred plan, the total cost is given by the equation: $300 + $1.50x.

For the basic plan, the total cost is given by the equation: $25 + $5x.

Setting the two equations equal to each other, we get: $300 + $1.50x = $25 + $5x.

Simplifying the equation, we have: $275 = $3.50x.

Dividing both sides of the equation by $3.50, we get: x = 78.57. Rounded to the nearest whole number, the number of visits when the preferred plan and basic plan will cost the same is 79 visits.