Jack borrowed his father\'s luxury car and promised to return it with a full tan

Question

Jack borrowed his father's luxury car and promised to return it with a full tank of premium gas, which costs $2.50 per gallon. From experience, he knows that he needs 15.5 gallons. But he only has $38, which isn't enough. He decides to get as much premium as possible and fill the remainder of the tank with regular gas, which costs $2.30 per gallon. To the nearest thousandth of a gallon, how much of each type of gas should he get?

I am not sure how to set up this problem. I came up with the following, but I'm not sure whether it is correct:
2.50x + 2.30 (15.5 - x) = 38
Please help.

Explanation / Answer

The equation that you set up is correct. Simply solve for x to find the number of gallons of premium gas, and subtract that number from 15.5 to find the number of gallons of regular gas.

2.5x+2.3(15.5-x)=38

2.5x+35.65-2.3x=38

.2x=2.35

x=11.75    (premium gas)

15.5-11.75=3.75 (regular gas)

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