Need help with a gym math problem..

Question

A gym charges a fee to join plus a monthly fee. Joining plus three months costs $160. Joining plus five months costs $200. Write a system of equations that describes the given situation. Use j for the joining fee and m for the number of months.

All the help would be much appreciated.

Answer 1

Hello,

To solve this problem, we can write the information they give us in the form of two equations. "J" is our joining fee, and "m" is the number of months at the gym.

Joining, plus three months, can be written as "j" for joining fee, plus 3 times the monthly fee.

This all equals $160 as they tell us. So, we can write this "sentence" as:

j + 3m = 160

Likewise, the joining fee, "j" plus 5 times the monthly fee, 5 times "m," equals $200. This can be written as:

j + 5m = 200

Now we have our system of equations, as shown below.

j + 3m = 160

j + 5m = 200

We can now solve this using the elimination method. We can subtract the second line from the first one to cancel out the J and solve for M.

j-j = 0, cancels out

3m - 5m = -2m

160 - 200 = -40

Which will give us:

-2m = -40.

If we divide both sides by -2 to isolate the m, we will get:

m = 20.

Now we know that m = 20, so the monthly fee is $20.

To solve for the joining fee, j, we will plug m = 20 back into the first line of the system, j + 3m = 160

Substituting m for 20 will give us j + 3(20) = 160

j + 60 = 160

Then, subtract 60 from both sides.

j = 160 - 60

j = 100

So, our joining fee "j" is 100 dollars.

Answer 2

F +3M = 160

F +5M =200

subtract 1st equation from 2nd

2M =40

M= $20 Month fee

F=160-3(20)= $100 Fee to join

Answer 3