SOLUTION: A family has two cars. The first car has a fuel efficiency of miles per gallon of gas and the second has a fuel efficiency of miles per gallon of gas. During one particular week,

Question 566607: A family has two cars. The first car has a fuel efficiency of miles per gallon of gas and the second has a fuel efficiency of miles per gallon of gas. During one particular week, the two cars went a combined total of miles, for a total gas consumption of 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!
your formula is:
bx + a(m-x) = abm/c
a = miles per gallon of the first car.
b = miles per gallon of the second car.
c = combined mileage of both cars.
m = total miles traveled by both cars.
x = total miles traveled by first car.
m-x = total miles traveled by second car.
number of combined gallons consumed is equal to m/c
number of gallons consumed by first car is x/a
number of gallons consumed by second car is (m-x)/b
let's see how it works.
assume both cars traveled 1500 miles.
assume first car gets 20 miles per gallon.
assume second car gets 35 miles per gallon.
assume the combined mileage is 25 miles per gallon.
you want to know how many gallons was consumed by first car and how many gallons was consumed by second car.
the formula is:
bx + a(m-x) = abm/c
you are given:
a = 20
b = 35
c = 25
m = 1500
substitute in the equation to get:
35x + 20(1500-x) = 20*35*1500/25
simplify this equation to get:
35x + 30000 - 20x = 42000
combine like terms to get:
15x + 30000 = 42000
subtract 30000 from both sides of this equation to get:
15x = 42000 - 30000
simplify to get:
15x = 12000
divide both sides of this equation by 15 to get:
x = 800
since m = 1500 and x = 800, this means that:
m-x = 700
you now have:
x = 800
m-x = 700
x is the number of miles traveled by the first car.
m-x is the number of miles traveled by the second car.
the number of gallons consumed by the first car is x/a which is equal to 800/20 which is equal to 40.
the number of gallons consumed by the second car is (m-x)/b which is equal to 700/35 which is equal to 20.
total gallons consumed by both cars is 40 + 20 = 60.
both cars traveled 1500 miles total at a combined efficiency of 25 miles per gallon.
combined gallons consumed is equal to m/c which is equal to 1500/25 which is equal to 60 gallons.
the calculations for gallons consumed are the same so the values for x and m-x must be good.
the formula works for any combined miles and combined miles per gallon as long as you know the miles per gallon of the first car and the miles per gallon of the second car as well.

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