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A family has two cars. The first car has a fuel efficiency of 28 miles per gallon of gas and the second has a fuel efficiency of 34 miles per gallon of gas.
During one particular week, the two cars went a combined total of 2100 miles, for a total gas consumption of 85 gallons. How many gallons were consumed by each of the two cars that week?
Gas Equation: x + y = 85 gallons
Distance Eq: 28x+34y = 2100 miles
Multiply thru the gas eq by 28 to get:
28x + 28y = 28*85
Subtract that from the distance Eq. and solve for "y":
6y = -280
y = 46 2/3 gallons (amt. consumed by the 34 mpg car)
x = 85-46 2/3 = 38 1/3 gallons (amt. consumed by the 28 mpg car)