SOLUTION: Please let me know step by step - thanks! Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 mi

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Question 593731: Please let me know step by step - thanks!
Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

let him drive x miles on Highway
y miles in city
Total miles traveled
x+y = 397..........(1)
Consumption on Highway + consumption in city = Total consumption
x/36 + y/31= 12
31x+36y= 12*31*36
3136yy =13392.........(2)
x miles on highway
y miles in city

1 x + 1 y = 397 .............1

31.00 x + 36.00 y = 13392 .............2
Eliminate y
multiply (1)by -36
Multiply (2) by 1
-36 x -36 y = -14292
31.00 x + 36 y = 13392
Add the two equations
-5.00 x = -900
/ -5.00
x = 180.00
plug value of x in (1)
1.00 x + 1.00 y = 397.00
180.00 + 1.00 y = 397.00
1.00 y = 397.00 + -180.00
1.00 y = 217.00
y = 217.00
180 miles on highway
217 miles in city
m.ananth@hotmail.ca