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

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

Gym a:

$65 + $20 per month

$65 + 20m m=month

gym b:

$25 + $35 per month with 20% discount

$25 + $28m