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.