Question

"My car gets 30 miles per gallon when I drive on the highway and 25 miles per gallon when I drive in the city. How many highway miles do I drive on a 400-mile trip if the car consumes 14 gallons of gasoline during this trip?"

Answer 1

300 miles

Explanation:

Let the gallons of fuel used on highway be X

gallons of fuel used in city be Y

Given that total no of gallons consumed on trip is 14

hence

X + Y = 14 -----------------------equation A

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Given

no. of miles car can drive on highway using 1 gallon of fuel = 30

therefore

no. of miles car can drive on highway using X gallon of fuel = 30X

no. of miles car can drive in city using 1 gallon of fuel = 25

therefore

no. of miles car can drive in city using Y gallon of fuel = 25Y

Given that total miles driven on trip is 400 miles

therefore

30X + 25 Y = 400 ---------------------------------equation B

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now we have two equation

X + Y = 14 -----------------------equation A

Y = 14 - X -----------------------equation C

30X + 25 Y = 400 ---------------------------------equation B

substituting value of Y from equation C in equation B we have

30X + 25 Y = 400

=> 30X + 25 (14 - X) = 400

=>30X + 350 - 25X = 400

=> 5X = 400 - 350 = 50

=> X = 50/5 = 10

Y = 14 - X = 14 - 10 = 4

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now we have to find miles drove on highway

we have defined above

no. of miles car can drive on highway using X gallon of fuel = 30X

where X is no of gallons of fuel used on highway

therefore

no. of miles car can drive on highway using X gallon of fuel = 30*10 = 300