Question

Isaac wants to join a gym. He checked out the membership fees at two gyms.

Gym A charges a new member fee of $65 and $20 per month.
Gym B charges a new member fee of $25 and $35 per month, but Isaac will get a discount of 20% on the monthly fee

Answer 1

gym a:
$65 + $20 per month
$65 + 20m m=month

gym b:
$25 + $35 per month with 20% discount
$25 + $28m

Answer 2

Gym A charges a new member fee of $65 and $20 per month.
When you see 'per' in a problem, it usually means the next word will be the variable in the equation. The next word is 'month' so use 'm' as the variable.
This gives you: 20m
Gym A doesn't charge you 65 per anything, so it is just on it's own.
This gives you: +65
Add these parts together to get:
20m + 65

Gym B charges a new member fee of $25 and $35 per month, but Isaac will get a discount of 20% on the monthly fee.
First thing's first, find 20% of 35, the monthly fee.
35 * .8 = 28
( I got .8 because .8 = 80% which would be what price is left )
The monthly fee is 28. Monthly fees are 'per month' so it will be 'm' again.
This gives you: 28m
The new member fee doesn't have 'per month' so it's on it's own.
This gives you: +25
Put them together and bam,
28m + 25

Now that you have both equations, put them on either side of an equal signs, so you can find when they are equal.
28m + 25 = 20m + 65
Solve the equation.
28m + 25 = 20m + 65
-20m -20m
8m + 25 = 65
-25 -25
8m = 40
/8 /8
m= 5
When the membership is 5 Months, they are equal