Word problem for algebra I. Needs to write equation and answer

Question

A shoppers discount card charges a monthly fee of $15 and sells gas for $2.05 a gallon.  The gas station across the street sells gas for $2.35 a gallon and charges no fee.  How many gallons of gas would you have to buy in one month to spend the same amount at either store?

Answer 1

Here's what we know:

m = 2.05g + 15 (the money spent in one place is $2.05 a gallon plus $15 for the discount)

m = 2.35g (the second place charges a straight $2.35 per gallon)

 

Since we're looking for the same amount spent, we need the two equations to equal one another:

2.05g + 15 = 2.35g

Now to isolate g. Subtract 2.05g from both sides:

2.05g + 15 - 2.05g = 2.35g - 2.05g

15 = .3g

Divide by .3:

15 / .3 = .3g / .3

50 = g

 

So you need to purchase 50 gallons to equal one another