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A gas station sells three types of gas: Regular for $2.95 a gallon, Performance Plus for $3.15 a gallon, and Premium for $3.35 a gallon. On a particular day 4300 gallons of gas were sold for a total of $13,305. Two times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day?

User Hronro
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1 Answer

3 votes

Answer:

3400 gallons of Regular gas, 900 gallons of Performance Plus gas, and 1200 gallons of Premium gas were sold

Explanation:

To solve this problem, let's assign variables to represent the number of gallons sold for each type of gas.

Let's say:

- R represents the number of gallons of Regular gas sold.

- P represents the number of gallons of Performance Plus gas sold.

- M represents the number of gallons of Premium gas sold.

From the information given, we can create the following equations:

Equation 1: The total number of gallons sold is 4300: R + P + M = 4300

Equation 2: The total cost of gas sold is $13,305: 2.95R + 3.15P + 3.35M = 13,305

Equation 3: Two times as many gallons of Regular as Premium gas were sold: R = 2M

Now, let's solve the system of equations:

Using Equation 3, we can substitute R in Equation 1:

2M + P + M = 4300

3M + P = 4300

Next, let's substitute R in Equation 2:

2.95(2M) + 3.15P + 3.35M = 13,305

5.9M + 3.15P + 3.35M = 13,305

9.25M + 3.15P = 13,305

Now we have a system of two equations with two variables:

3M + P = 4300

9.25M + 3.15P = 13,305

To solve this system, we can use either substitution or elimination method. Let's use the substitution method:

From Equation 1, we have P = 4300 - 3M. We can substitute this value into Equation 2:

9.25M + 3.15(4300 - 3M) = 13,305

9.25M + 13545 - 9.45M = 13,305

-0.2M = -240

M = 1200

Now that we know the value of M, we can substitute it back into Equation 1 to find R:

R + P + M = 4300

R + (4300 - 3M) + M = 4300

R + 4300 - 3600 + 1200 = 4300

R + 900 = 4300

R = 3400

Finally, we can find P using Equation 3:

R = 2M

3400 = 2(1200)

3400 = 2400

P = 900

Therefore, on that particular day, 3400 gallons of Regular gas, 900 gallons of Performance Plus gas, and 1200 gallons of Premium gas were sold.

User Racooon
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