SOLUTION: My car gets 17 miles per gallon in the city and 45 miles per gallon on the highway. Suppose I used 12.174 gallons of gas and got an average of 22 miles per gallon for the trip.

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Question 916938: My car gets 17 miles per gallon in the city and 45 miles per gallon on the highway. Suppose I used 12.174 gallons of gas and got an average of 22 miles per gallon for the trip.
How many gallons did I use for each part of the trip?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates, fuel consumption.
RV=D for rate, fuel volume, distance; V is gallons, D is miles.


________________rate__________volume___________distance
CITY____________17
HWY_____________45
Totals__________22____________12.174

Assign variables, first impulse is for trying the volumes.

________________rate__________volume___________distance
CITY____________17______________x_______________17x
HWY_____________45______________y_______________45y
Totals__________22____________12.174___________(22)(12.174)

The rest of the table cells are also filled with proper expressions or numbers. This table indicates two linear equations in the unknown volume variables, x and y.

highlight_green%28system%28x%2By=12.174%2C17x%2B45y=%2822%29%2812.174%29%29%29

Solve that system.