SOLUTION: A hybrid car gets 60 miles per gallon of gas in the city and 51 miles per gallon on the highway. During the week, the hybrid uses 12 gallons of gas and travels 675 miles. How m

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Question 516150: A hybrid car gets 60 miles per gallon of gas in the city and 51 miles per gallon on
the highway. During the week, the hybrid uses 12 gallons of gas and travels 675 miles. How many miles did the hybrid drive in the city? How many miles were driven on the highway?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = miles driven in city
Let b = miles driven on highway
given:
(1) +a+%2B+b+=+675+
(2) +a%2F60+%2B+b%2F51+=+12+
------------------
Multiply both sides of (2) by +60%2A51+
(2) +51a+%2B+60b+=+12%2A60%2A51+
(2) +51a+%2B+60b+=+36720+
Multiply both sides of (1) by +51+
and subtract (1) from (2)
(2) +51a+%2B+60b+=+36720+
(1) +-51a+-+51b+=+-34425+
+9b+=+2295+
+b+=+255+
and, since
(1) +a+%2B+b+=+675+
(1) +a+=+675+-+255+
(1) +a+=+420+
420 miles are driven in city
255 miles are driven on highway
check answer:
(2) +a%2F60+%2B+b%2F51+=+12+
(2) +420%2F60+%2B+255%2F51+=+12+
(2) +7+%2B+5+=+12+
(2) +12+=+12+
OK