Question

Casey wants to buy a gym membership. One gym has a $120 joining fee and costs $35 per month. Another gym has no joining fee and costs $55 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?After____months, Casey would have paid $____at either gym.

Answer 1

Answer:

After 6 months, Casey would have paid $330 at either gym.

Explanation:

Let the number of months be represented by the variable t.

One gym has a $120 joining fee and costs $35 per month.

The equation representing the amount paid for this gym is:

$f(t)=120+35t$

Another gym has no joining fee and costs $55 per month.

The equation representing the amount paid for this gym is:

$g(t)=55t_{}$

When the amount to be a member is the same, we have that:

$\begin{gathered} f(t)=g(t) \\ 120+35t=55t \end{gathered}$

We solve for t.

$\begin{gathered} 120=55t-35t \\ 120=20t \\ t=\frac{120}{20} \\ t=6\text{ months} \end{gathered}$

The amount that would have been paid will be:

$\begin{gathered} f(6)=120+35(6) \\ =120+210 \\ =\ 330 \end{gathered}$

After 6 months, Casey would have paid $330 at either gym.