Help please

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 20 miles per gallon of gas. The two cars combined a total of 1200 miles for a total gas consumption of 45 gallons. How many gallons were  consumed by each car that week 

Answer 1

Miles/Gal * Gal = Miles

If the car that has 30 mpg uses x gallons then

the car that has 20 mpg use 45-x gallons

 

(30 m/g)(x gal) + (20 m/g)(45-x gal) = 1200

 

30x + 20(45-x) = 1200

30x + 900 - 20x = 1200

 

Solve for x to get the gallons used by the car with 30 mpg efficiency.

Subtract that from 45 to get the gallons used by the car with 20 mpg efficiency.

Answer 2

First step in a word problem like this is to assign variables.  Since we're looking for the gallons consumed by each car, let A be the gallons consumed by the first and B be the gallons consumed by the second.  Then, distance will be mileage times fuel consumed, so

 

Distance by first car = 30A

Distance by second car = 20B

 

We know that the total was 45 gallons, so

 

A + B = 45

 

and we know that the total distance was 1200 miles, so

 

30A + 20B = 1200

 

If we solve the first equation for A, we get

 

A = 45 - B

 

We can then substitute this into the second equation to get

 

30(45 - B) + 20B = 1200

1350 - 30B + 20B = 1200      (multiplying out the parenthesis)

-10B = -150                        (subtracting 1350 from both sides and simplifying)

B = 15                                (dividing by -10)

 

Therefore,

 

A = 45 - B = 45 - 15 = 30

 

To doublecheck our work, we see that A + B = 30 + 15 = 45 and that

 

30A + 20B = 30*30 + 20*15 = 900 + 300 = 1200.

 

So the first car used 30 gallons and the second car used 15 gallons.

 

If you still have any questions on that, please let me know.