Question

a family has two cars. the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. during one particular week, the two cars went a combined total of 1525 miles, for a total gas consumption of 50 gallons. how many gallons were consumed by each of the two cars that week? first car: square gallons second car: square gallons

Explanation:

Step1: Define variables for gallons

Let $x$ = gallons used by first car, $y$ = gallons used by second car.

Step2: Set up total gallons equation

Total gas used is 50 gallons:
$x + y = 50$

Step3: Set up total miles equation

Miles = efficiency × gallons, total miles = 1525:
$20x + 35y = 1525$

Step4: Solve for $x$ from Step2

Rearrange total gallons equation:
$x = 50 - y$

Step5: Substitute $x$ into miles equation

Substitute $x=50-y$ into $20x + 35y = 1525$:
$20(50 - y) + 35y = 1525$
$1000 - 20y + 35y = 1525$
$1000 + 15y = 1525$

Step6: Solve for $y$

Isolate $y$:
$15y = 1525 - 1000$
$15y = 525$
$y = \frac{525}{15} = 35$

Step7: Solve for $x$

Substitute $y=35$ into $x=50-y$:
$x = 50 - 35 = 15$

Answer:

First car: 15 gallons
Second car: 35 gallons