Question

There are two different memberships at the gym. One of the plans charges $5 per month and $4 each day you work out. The other plan charges $32 per month and $1 each day you work out. After how many days of workouts would the membership plans be the same price?(1 point) Responses After 3 days of workouts the price for the two plans would be equal. After 3 days of workouts the price for the two plans would be equal. After 7 days of workouts the price for the two plans would be equal. After 7 days of workouts the price for the two plans would be equal. After 9 days of workouts the price for the two plans would be equal. After 9 days of workouts the price for the two plans would be equal. After 2.8 days of workouts the price for the two plans would be equal.

Answer 1

Let's denote the number of days worked out as \( x \).

We can set up the equations for both membership plans based on their pricing structures:

**Plan 1:**
- Monthly fee: $5
- Daily fee: $4
- Total cost after \( x \) days: \( 5 + 4x \)

**Plan 2:**
- Monthly fee: $32
- Daily fee: $1
- Total cost after \( x \) days: \( 32 + 1x \)

To find the number of days after which the two plans cost the same, we set the total costs equal to each other:

\[
5 + 4x = 32 + 1x
\]

Now, let's solve for \( x \):

1. Subtract \( 1x \) from both sides:
\[
5 + 4x - 1x = 32
\]
This simplifies to:
\[
5 + 3x = 32
\]

2. Subtract 5 from both sides:
\[
3x = 32 - 5
\]
Simplifying gives:
\[
3x = 27
\]

3. Divide both sides by 3:
\[
x = \frac{27}{3} = 9
\]

So, the membership plans would be the same price after 9 days of workouts.

The correct response is: **After 9 days of workouts the price for the two plans would be equal.**