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)

Question

Responses

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 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 2.8 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.

After 3 days of workouts the price for the two plans would be equa

Answer 1

To compare the costs of the two gym membership plans, we can set up equations for the total cost of each plan based on the number of days worked out, denoted as \(d\).

1. For the first plan: \[ \text{Cost}_1 = 5 + 4d \] (where $5 is the monthly fee and $4 is the daily fee)

2. For the second plan: \[ \text{Cost}_2 = 32 + 1d \] (where $32 is the monthly fee and $1 is the daily fee)

We need to find the value of \(d\) when the costs are equal: \[ 5 + 4d = 32 + 1d \]

Next, we simplify the equation: \[ 5 + 4d = 32 + 1d \] Subtract \(1d\) from both sides: \[ 5 + 3d = 32 \] Subtract 5 from both sides: \[ 3d = 27 \] Now, divide both sides by 3: \[ d = 9 \]

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