Question

Sarah wants to join a gym. Fitness Gym charges a $120 enrollment fee and $25 a month. Sports Gym charges no enrollment fee and $45 a month. Sarah wants to know how many months it will take for the cost of both gyms to be the same. She writes the two equations C = 120 + 25x and C = 45x and graphs the solution. What does the graph tell her about many months it will take?

A) It will take 5 months.
B) It will take 6 months.
C) It will take 9 months.
D) It will take 18 months.

Answer 1

it will take about 6 months

Answer 2

B) It will take 6 months.

Explanation:

This problem can be solved using the equation or the graph.

The given equation is

`120+25x=45x`

We solve for
`x`

`120=45x-25x\\120=20x\\x=(120)/(20)\\ x=6`

This means after 6 months both gyms will cost the same.

Now, if you wanna solve this using the graph, you just need to look for the interception points of the two lines, where each of them represents each gym. Notice that they intercept at (6,270), that is, after 6 months they cost $270 each of them.

Therefore, the right answer is B).