Question

A gas station sells three types of gas: regular for $3.00 a gallon, performance plus for $3.20 a gallon, and premium for $3.40 a gallon. on a particular day 3700 gallons of gas were sold for a total of $11,620. two times as many gallons of regular as premium gas were sold. how many gallons of each type of gas were sold that day?

Answer 1

On that day, 2200 gallons of regular gas, 400 gallons of performance plus gas, and 1100 gallons of premium gas were sold at the gas station.

Step-by-step explanation:

Let's represent the number of gallons of regular, performance plus, and premium gas sold as:

R = number of gallons of regular gas

P = number of gallons of performance plus gas

Pr = number of gallons of premium gas

We are given that two times as many gallons of regular as premium gas were sold. This can be represented as:

R = 2Pr

Also, we are given that a total of 3700 gallons of gas were sold for a total of $11,620. This can be represented as:

3R + 3.2P + 3.4Pr = 11620

From these two equations, we can solve for the values of R, P, and Pr:

Substituting the value of R from the first equation into the second equation:

3(2Pr) + 3.2P + 3.4Pr = 11620

6Pr + 3.2P + 3.4Pr = 11620

9.4Pr + 3.2P = 11620

Now we know that the sum of the three types of gas sold is equal to 3700 gallons:

R + P + Pr = 3700

Substituting the value of R from the first equation into the third equation:

2Pr + P + Pr = 3700

3Pr + P = 3700

Now we have a system of two equations with two variables. Solving this system will give us the values of P and Pr, which we can then use to find the value of R.

From the first equation:

3Pr + P = 3700

P = 3700 - 3Pr

Substituting this value of P into the second equation:

9.4Pr + 3.2(3700 - 3Pr) = 11620

9.4Pr + 11840 - 9.6Pr = 11620

-0.2Pr = -220

Pr = 1100

Substituting this value of Pr into the equation P = 3700 - 3Pr:

P = 3700 - 3(1100)

P = 3700 - 3300

P = 400

Finally, substituting the values of Pr and P into the equation R = 2Pr:

R = 2(1100)

R = 2200

Therefore, 2200 gallons of regular gas, 400 gallons of performance plus gas, and 1100 gallons of premium gas were sold that day.

Answer 2

A gas station sells three types of gas: Regular for $2.90 a gallon, Performance Plus for $3.05 a gallon, and Premium for $3.20 a gallon. On a particular ... for $3.20 a gallon. On a particular day 5000 gallons of gas were sold for a total of $14,920. Three times as many gallons of Regular asPremium gas were sold.