SOLUTION: 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 40 miles per gallon of gas. During one particular w

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Question 991101: 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 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 2000 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
first car gets 15 miles per gallon.
second car gets 40 miles per gallon.
both cars went a total of 2000 miles for a total gas consumption of 75 gallons.

miles driven by first car is x.
miles driven by second car is y.

gallons consumed by first car is x / 15.
gallons consumed by second car is y / 40.

you have 2 equations.

x + y = 2000
x/15 + y/40 = 75

use the first equation to solve for y.

you get y = 2000 - x

replace y with 2000 - x in the second equation to get:

x/15 + (2000 - x) / 40 = 75

remove the fractions by multiplying both sides of the equation by 120.

you get:

120 * x / 15 + 120 * (2000 - x) / 40 = 75 * 120

simplify to get:

8 * x + 3 * (2000 - x) = 9000

simplify further by removing parentheses to get:

8 * x + 6000 - 3 * x = 9000

subtract 6000 from both sides of the equation to get:

8 * x - 3 * x = 3000

combine like terms to get:

5 * x = 3000

divide both sides of the equation by 5 to get:

x = 600

since y = 2000 - x, this means that:

y = 1400

the first car traveled 600 miles.
the second car traveled 1400 miles.

600 + 1400 = 2000
600 / 15 + 1400 / 40 = 40 + 35 = 75

numbers check out.

your solution is the the first car traveled 600 miles at 15 miles per gallon and the second car traveled 1400 miles at 40 miles per gallon.