Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. jen wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. with the first membership plan, jen can pay $35 per month, plus $1 for each group class she attends. alternately, she can get the second membership plan and pay $33 per month plus $3 per class. if jen 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 jen takes __ classes per month.

Explanation:

Step1: Define variables

Let $x$ be the number of classes per month and $y$ be the total cost.
For the first plan, the cost equation is $y = 35 + 1\times x=35 + x$.
For the second plan, the cost equation is $y = 33+3\times x = 33 + 3x$.

Step2: Set the two equations equal

Since the two - plans cost the same, we set $35 + x=33 + 3x$.
Subtract $x$ from both sides: $35=33 + 3x-x$, which simplifies to $35=33 + 2x$.
Subtract 33 from both sides: $35 - 33=2x$, so $2 = 2x$.
Divide both sides by 2: $x = 1$.

Step3: Find the total cost

Substitute $x = 1$ into the first equation $y=35 + x$.
$y=35 + 1=36$.

Answer:

Each membership plan costs $\$36$ if Jen takes $1$ classes per month.