Question

A gas station sells regular gas for $2.30 per gallon and premium gas for $2.80 a gallon. At the end of a business day 290 gallons of gas had been sold, and receipts $702. How many gallons of each type of gas had been sold?

Answer 1

There are two prices for different types of gas:

$2.30 per gallon of regular gas, and

$2.80 per gallon of premium gas.

At the end of the day 290 gallons were sold, and the receipts totaled $702.

We are asked how many gallons of each gas were sold. Since these are our unknowns, we named them:

gallons of regular: R

gallons of premium : P

So we create two equations:

Equation 1: P + R = 290

since we know that the total number of gallons sold was 290

Equation 2: 2.3 R + 2.8 P = 702

where we add the $ amounts produced by selling R gallons of the regular (priced at $2.30 per gallon) --> 2.30 * R = 2.3 R

and P gallons of the premium (priced at $2.8 per gallon) --> 2.80 * P = 2.8 P

Now, we use equation 1 to solve for one of the unknown, let's say solve for P:

P = 290 - R

we use this as our "substitution equation" which allows us to replace p with (290 - R) in the second equation:

2.3 R + 2.8 (290 - R) = 702

now we solve for R:

2.3 R + 812 - 2.8 R = 702

we combine the terms on R on the left:

-0.5 R + 812 = 702

now we subtract 812 from both sides:

-0.5 R = 702 - 812

-0.5 R = -110

R = 220 gallons

Then we find the number of gallons for the premium by using the substitution equation:

P = 290 - R = 290 - 220 = 70 gallons

So there were 220 gallons of regular sold, and 70 gallons of premium gas.