A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?

Question

Mathematics

Amber Mayer

12 May, 08:36

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?

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Answers (1)

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Rihanna Schmitt · Answer 1

15x+25y=975

x+y=55

Rearrange equation two so x is by itself.

x=-y+55

Plug the rearranged equation two into equation one.

15 (-y+55) + 25y=975

Evaluate the 'new' equation 1.

-15y+825+25y=975

10y+825=975

10y=150

y=15

Choose an equation to evaluate with y to get x. (i chose equation 2 because it was easier)

x+15=55

Evaluate the equation

x=55-15

x=40

So now we have x=40 and y=15

Evaluate those two terms with both equations to check the correctness.

15 (40) + 25 (15) = 975

600+375=975

975=975 (correct)

40+15=55

55=55 (correct)

Both equations are correct so the values of x and y are true.