My car gets 19 miles per gallon in the city and 34 miles per gallon on the highway. Suppose I used 12.857 gallons of gas and got an average of 27 miles per gallon for the trip.

Question

How many gallons did I use for each part of the trip?

_____gallons at 19 miles per gallon (if needed, round to 3 decimal places)

____ gallons at 34 miles per gallon (if needed, round to 3 decimal places)

Answer 1

put two unknowns x and y :
x is the number of liters of gasoline to move in the city
y is the number of liters of gasoline to move on the highway
x + y = 12.857 gallons
19x + 34y = 12,857.27 = 347.139
| 19x + 34y = 347.139
| x + y = 12.857
x = 6 gallon
y = 6.857 a gallon
gallons at 19 miles: x= 6 gallon
____ gallons at 34 miles: y = 6,857 gallon

Answer 2

thank you! but how did you get 347.139?

Answer 3

Total gas used for the trip = 12.857 gallons
rate for the whole trip = 27 mpg
so distance of trip = 27(12.857) miles = 347.139 miles

let the number of gallons used at the 19 mpg rate be x
then the number of gallons used at the 34 mpg rate be 12.857 - x

19x + 34(12.857 - x) = 347.139
19x + 437.138 - 34x = 347.139
-15x = -89.999
x = 6

so you used 6 gallons going at a rate of 19 mpg
and 6.857 gallons going at the 34 mpg rate