SOLUTION: A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular w

Algebra ->  Test -> SOLUTION: A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular w      Log On


   

Question 717935: A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 850 miles, for a total gas consumption of 35 gallons. How many gallons were consumed by each of the two cars that week?
First Car =
Second Car =
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles the 1st car travels
+850+-+d+ = distance in miles the 2nd car travels
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In words:
( miles ) / ( miles/gallon ) = gallons
Using this fact:
+d+%2F+30+%2B+%28+850+-+d+%29+%2F+20++=+35+
Multiply both sides by +60+
+2d+%2B+3%2A%28+850+-+d+%29+=+35%2A60+
+2d+%2B+2550+-+3d+=+2100+
+-d+=+-450+
+d+=+450+
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For 1st car:
gallons consumed = +d%2F30+
gallons consumed = +450%2F30+
gallons consumed = +15+
For 2nd car:
gallons consumed = +%28+850+-+d+%29%2F20+
gallons consumed = +%28+850+-+450+%29%2F20+
gallons consumed = +400%2F20+
gallons consumed = +20+
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check:
+15+%2B+20+=+35+
OK