Question

Community Gym charges a $50 membership fee and a $65 monthly fee. Workout Gym charges a $170 membership fee and a $55 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?

Answer 1

A) 12 months

B) $830

Explanation:

This question wants you to find the unknown variable in an algebraic equation. In order to do so, we need to interpret the word problem algebraically.

Let's break down what we have:

• Community Gym: $50 membership fee (one time fee) and a $65 monthly fee (recurring fee).
• Workout Gym: $170 membership fee (one time fee) and a $55 monthly fee (recurring fee).
• Now, a one time fee is self explanatory, it only occurs once. A recurring fee occurs every month. In other words, it's the fee amount times the number of months.

1. Let's set up equations for both gyms where
   `d` is the money paid (dependent variable) and
   `m` is the number of months (independent variable):

• Community Gym:
  `d=50+65m`
• Workout Gym:
  `d=170+55m`

2. We want the number of months (
`m`) when the money paid (
`d`) will be equal for both gyms. To find this, we'll set the two equations equal to each other to find the unknown variable
`m`:

• 
  `50+65m=170+55m\\ > 65m=120+55m\\ > 10m=120\\ > m=12`
• This gives us the time, in months, when the money paid for both gyms is equal.

3. To find the money paid
`d`, substitute m=12 into either equation:

• 
  `d=50+65(12)=830\\OR\\d=170+55(12)=830`

we can see that d is the same for both equations, and is equal to $830.