SOLUTION: Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many mile

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many mile      Log On


   



Question 672706: Julio has found that his new car gets 36 miles per gallon on the highway
and 31 miles per gallon in the city. He recently drove 397 miles on 12
gallons of gasoline. How many miles did he drive on the highway? How
many miles did he drive in the city?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
( miles/gallon ) x ( gallons used ) = miles driven
Let +a+ = gallons used on highway
Let +b+ = miles driven on highway
On highway:
(1) +36a+=+b+
In city:
(2) +31%2A%28+12+-+a+%29+=+397+-+b+
---------------------------
(2) +372+-+31a+=+397+-+b+
(2) +b+-+31a+=+25+
Substitute (1) into (2)
(2) +36a+-+31a+=+25+
(2) +5a+=+25+
(2) +a+=+5+
+12+-+a+=+7+
and
(1) +b+=+36%2A5+
(1) +b+=+180+
+397+-+b+=+397+-+180+
+397+-+b+=+217+
He drove 180 mi on the highway
he drove 217 mi in the city
-----------------------
check:
(2) +31%2A%28+12+-+a+%29+=+397+-+b+
(2) +31%2A%28+12+-+5+%29+=+397+-+b+
(2) +31%2A7+=+397+-+b+
(2) +b+=+397+-+217+
(2) +b+=+180+
OK