Question

a gas station sells regular gas for $2.20 per gallon and premium gas for $2.70 a gallon. at the end of a business day 270 gallons of gas had been sold, and receipts totaled $644. how many gallons of each type of gas had been sold?

Answer 1

To solve for how many gallons of regular and premium gas were sold, a system of two linear equations was set up and solved using substitution. It was determined that 170 gallons of regular gas and 100 gallons of premium gas were sold.

Step-by-step explanation:

The question involves solving a system of linear equations to find out how many gallons of regular and premium gas were sold. We have two unknowns: the number of gallons of regular gas (let's call it R) and the number of gallons of premium gas (let's call it P). We are given that the total number of gallons sold is 270, so we have the equation R + P = 270.

We're also given that the total receipts amounted to $644, and regular gas sells for $2.20 per gallon while premium gas sells for $2.70 per gallon, leading to the equation 2.20R + 2.70P = 644. We can solve this system of equations using substitution or elimination methods.

1. Write down the system of equations:
   R + P = 270
   2.20R + 2.70P = 644
2. Choose an equation to solve for one variable, let's use the first equation and express R as: R = 270 - P.
3. Substitute R in the second equation and solve for P:
   2.20(270 - P) + 2.70P = 644
4. Simplify and solve the equation:
   594 - 2.20P + 2.70P = 644
   0.50P = 644 - 594
   0.50P = 50
   P = 50 / 0.50
   P = 100
5. Now that we have P, substitute it back into R = 270 - P to find R:
   R = 270 - 100
   R = 170

Therefore, 170 gallons of regular gas and 100 gallons of premium gas were sold.