SOLUTION: A salesperson purchased an automobile that was advertised as averaging 27mi/gal in the city and 38 mi/gal on the highway. A recent trip covered 2142 miles required 61 gallons of ga

Question 714158: A salesperson purchased an automobile that was advertised as averaging 27mi/gal in the city and 38 mi/gal on the highway. A recent trip covered 2142 miles required 61 gallons of gasoline. Assuming that the advertised mileage estimates were correct, ho many miles were driven in the city?

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Great exercise problem. It's another kind of Rate*Q=M type relation where the units of R is that of M divided by that of Q; just like rate, time, distance, or rate, time, job-task; but now we would use Rate*Volume=Distance.

This table helps us to see all the values and expressions for the city and the highway driving:

PICKING THESE VARIABLES:
LET c = volume of fuel used on city roads
LET h = volume of fuel used on highway roads

ROAD TYPE_____________Rate mi/gal_________Volume gal.s__________Distance, mi
City__________________27___________________c____________________(____)
Highway_______________38___________________h____________________(____)

Check that table and be sure you understand how values and variables were decided and placed. The quantities or expressions for distances still need to be filled in. Distance is Rate multiplied by Volume of fuel; miles per gallon, multiplied by gallons, is MILES.
We are also given some driving data about fuel the salesman used and total miles driven; we'll put that in the table also:

ROAD TYPE_____________Rate mi/gal_________Volume gal.s__________Distance, mi
City__________________27___________________c____________________(27*c)
Highway_______________38___________________h____________________(38*h)
TOTAL____________________________________61_____________________2142

You should see now how to take TWO equations from this arrangement of data.

SYSTEM TO SOLVE FOR c AND h:

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