SOLUTION: the honda civic hybrid vehicle, powered by gasoline-electric technology, gets 49 mpg in city driving and 51mpg in highway driving. the car is driven 447 miles on 9 gallons of gasol

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the honda civic hybrid vehicle, powered by gasoline-electric technology, gets 49 mpg in city driving and 51mpg in highway driving. the car is driven 447 miles on 9 gallons of gasol      Log On


   

Question 778224: the honda civic hybrid vehicle, powered by gasoline-electric technology, gets 49 mpg in city driving and 51mpg in highway driving. the car is driven 447 miles on 9 gallons of gasoline. how many miles were driven in the city and how many were driven on the highway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of miles driven in the city
+447+-+x+ = miles driven on highway
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Note that:
( miles driven ) / ( miles / gallon ) = ( gallons used )
I can say:
+x+%2F+49+%2B+%28+447+-+x+%29+%2F+51++=+9+
Multiply both sides by +49%2A51+
+51x+%2B+49%2A%28+447+-+x+%29+=+9%2A49%2A51+
+51x+%2B+21903+-+49x+=+22491+
+2x+=+22491+-+21903+
+2x+=+588+
+x+=+294+
+447+-+294+=+153+
294 miles were driven in the city
153 miles were driven on highway
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check:
+x+%2F+49+%2B+%28+447+-+x+%29+%2F+51++=+9+
+294+%2F+49+%2B+153+%2F+51++=+9+
++6+%2B+3+=+9+
+9+=+9+
OK