SOLUTION: Andea's car averages 18.4 mi/gal in city driving and 25.8 mi/gal in highway driving. if she drove a total of 652.0 mi on 29 gal of gas, how many of the gallons were used for city d

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Andea's car averages 18.4 mi/gal in city driving and 25.8 mi/gal in highway driving. if she drove a total of 652.0 mi on 29 gal of gas, how many of the gallons were used for city d      Log On


   

Question 242412: Andea's car averages 18.4 mi/gal in city driving and 25.8 mi/gal in highway driving. if she drove a total of 652.0 mi on 29 gal of gas, how many of the gallons were used for city driving?
i think this a system of equations problem. i don't know how to set up the equations
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
YOU DON'T NEED A SYSTEM OF EQUATIONS;
THE FOLLOWING ONE WILL DO.
18.4X+25.8(29-X)=652
18.4X+748.2-25.8=652
-7.4X=652-748.2
-7.4X=-96.2
X=-96.2/-7.4
X=13 GAL CONSUMMED @ 18.4 MPH. CITY DRIVING.
29-13=16 GAL CONSUMMED @ 25.8 MPH.
PROOF:
18.4*13+25.8*16=652
239.2+412.8=652
652=652