Question

Donica wants to join a gym Gym A: $20 joining free and $40 monthly charge Gym B: No joining fee and $45 monthly charge Enter the number of months it will take for total cost for both gyms to be equal.

Answer 1

To find when the costs for both gyms are equal, we form equations for each gym's costs and solve for m, which represents the number of months. After setting up the equations and simplifying, we find that it will take 4 months for the costs to be equal.

Step-by-step explanation:

We need to determine when the total cost of joining and maintaining a membership at Gym A is equal to the cost of Gym B. Let's denote the number of months as m.

For Gym A, the total cost is the joining fee plus the monthly charge times the number of months: $20 + $40m.

For Gym B, there is no joining fee, so the total cost is simply the monthly charge times the number of months: $45m.

To find out when they equal each other, we set the two equations equal and solve for m:

• $20 + $40m = $45m

Simplifying this equation, we subtract $40m from both sides to get:

• $20 = $5m

Dividing both sides by $5, we determine the number of months:

• m = 4

So it will take 4 months for the total cost of both gyms to be equal.

Answer 2

Use equation in the form:

`C=mx+b`

Where C is the cost, m is the monthly charge, x is the number of months and b is the joining fee:

Gym A:

`C_A=40x+20`

Gym B:

`C_B=45x`

Find the number of months (x) that it rill take for CA and CB to be equal:

Equal CA and CB:

`\begin{gathered} C_A=C_B \\ \\ 40x+20=45x \end{gathered}`

Use the equation above to find the value of x:

`\begin{gathered} 40x-45x=-20 \\ -5x=-20 \\ x=(-20)/(-5) \\ \\ x=4 \end{gathered}`Then, it will take 4 months for total cost for both gyms to be equal