Question

a family has two cars. the first car has a fuel efficiency of 30 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 35 gallons. how many gallons were consumed by each of the two cars that week? first car: □ gallons second car: □ gallons

Explanation:

Step1: Define Variables

Let \( x \) be the gallons consumed by the first car, and \( y \) be the gallons consumed by the second car. We know two equations:

1. \( x + y = 35 \) (total gas consumption)
2. \( 30x + 25y = 975 \) (total miles driven, since miles = efficiency × gallons)

Step2: Solve the first equation for \( y \)

From \( x + y = 35 \), we get \( y = 35 - x \).

Step3: Substitute \( y \) into the second equation

Substitute \( y = 35 - x \) into \( 30x + 25y = 975 \):

$$ 30x + 25(35 - x) = 975 $$

Expand:

$$ 30x + 875 - 25x = 975 $$

Simplify:

$$ 5x + 875 = 975 $$

Subtract 875 from both sides:

$$ 5x = 100 $$

Divide by 5:

$$ x = 20 $$

Step4: Find \( y \)

Substitute \( x = 20 \) into \( y = 35 - x \):

$$ y = 35 - 20 = 15 $$

Answer:

First car: 20 gallons
Second car: 15 gallons