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 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 2.8 days of workouts the price for the two plans would be equal.

Answer 1

To find out after how many days of workouts the two membership plans would cost the same, we can set up an equation.

Let \( x \) be the number of days worked out.

For the first plan, the total cost \( C_1 \) can be expressed as: \[ C_1 = 5 + 4x \]

For the second plan, the total cost \( C_2 \) can be expressed as: \[ C_2 = 32 + 1x \]

We want to find \( x \) such that: \[ C_1 = C_2 \]

Setting the equations equal gives us: \[ 5 + 4x = 32 + 1x \]

Now, we can solve for \( x \):

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

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

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

Thus, the two 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.