A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1450 miles, for a total gas consumption of 40 gallons How many gallons were consumed by each of the two cars that week?

Question

A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1450 miles, for a total gas consumption of 40 gallons How many gallons were consumed by each of the two cars that week?

Note that the ALEKS graphing calculator can be used to make computations easier.
First car:_________gallons
second cars __________gallons

Answer 1

Let x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 40 - x.
The first car travels at a rate of 40 miles per gallon, so it travels 40x miles.
The second car travels at a rate of 30 miles per gallon, so it travels 30(40 - x) miles.
Together, the two cars travel a total of 1450 miles, so we have the equation:
40x + 30(40 - x) = 1450
40x + 1200 - 30x = 1450
10x + 1200 = 1450
10x = 250
x = 25
So, the first car consumed 25 gallons of gas, while the second car consumed 40 - 25 = 15 gallons of gas. Answer: \boxed{25} gallons, \boxed{15} gallons.