Question

write a system of equations to describe the situation below, solve using any method, and fill in the blanks. mike wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. with the first membership plan, mike can pay $34 per month, plus $3 for each group class he attends. alternately, he can get the second membership plan and pay $33 per month plus $4 per class. if mike attends a certain number of classes in a month, the two membership plans end up costing the same total amount. what is that total amount? how many classes per month is that? each membership plan costs $ if mike takes classes per month.

Explanation:

Step1: Set up the equations

Let \(x\) be the number of classes.
For the first plan: \(y = 34+3x\)
For the second plan: \(y = 33 + 4x\)

Step2: Solve the system of equations

Set \(34+3x=33 + 4x\)
Subtract \(3x\) from both sides: \(34=33 + 4x-3x\)
Simplify: \(34=33+x\)
Subtract \(33\) from both sides: \(x = 34 - 33=1\)

Step3: Find the total cost \(y\)

Substitute \(x = 1\) into \(y=34 + 3x\) (or \(y = 33+4x\))
\(y=34+3\times1=37\) (or \(y=33 + 4\times1=37\))

Answer:

Each membership plan costs \(\$37\) if Mike takes \(1\) classes per month.