197k views
4 votes
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?

1 Answer

2 votes

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.

User Rageit
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories