Question

or Kaylee wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Kaylee can pay $35 per month, plus $1 for each group class she attends. Alternately, she can get the second membership plan and pay $5 per month plus $4 per class. If Kaylee attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? Write a system of equations, graph them, and type the solution.

Answer 1

Sure, let's break this down.

First, let's set up the equations. We'll use 'x' to represent the number of classes Kaylee attends in a month.

For the first membership plan, the cost is $35 per month plus $1 per class. So, the equation would be:

C1 = 35 + x

For the second membership plan, the cost is $5 per month plus $4 per class. So, the equation would be:

C2 = 5 + 4x

We're looking for the point where the two costs are equal, so we set the two equations equal to each other and solve for 'x':

35 + x = 5 + 4x

Subtract 'x' from both sides and subtract '5' from both sides to get:

30 = 3x

Then divide both sides by '3' to solve for 'x':

x = 10

So, if Kaylee attends 10 classes in a month, the two membership plans will cost the same.

As for graphing these equations, I'm sorry I can't draw a graph here. But you can easily do it by plotting the two equations on a graph. The point where they intersect is the solution, which should be at (10, 45) - 10 classes for $45.

I hope this helps