SOLUTION: A salesperson purchased an automobile that was advertised as averaging 25 mi/gal in the city and 40 mi/gal on the highway. A recent sales trip that covered 1800 miles required 51

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Question 132875This question is from textbook
: A salesperson purchased an automobile that was advertised as averaging 25 mi/gal in the city and 40 mi/gal on the highway. A recent sales trip that covered 1800 miles required 51 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?


This question is from textbook

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
1800 total miles
51 gallons
25 miles per gallon city
40 miles per gallon highway

The total distance is the sum of the mileage of city and highway.
Let x be the number of gallons used for city driving. If so, then 51-x is the number of gallons used for highway.
Now setup an equation for the total mileage driven
Thus :
Total+=+highway+%2B+city+
1800+=+%2851-x%2940+%2B+x%2825%29+
1800+=+2040+-40x+%2B+25x+
-240+=+-15x+
+16+=+x+ Thus city driving used 16 gallons. To find the number of city miles, just multiply the number of gallons times the stated city rate of 25.
Yielding 400
Check your answer using highway milage to ensure the total is correct.
51-16 = 35
35 * 40 = 1400
total is 1400 + 400 = 1800!!