1. ## Word Problem

Is it ok if I ask another one? Its a different type of question.

In a family there are two cars. In a given week, the first car gets an average of 20 MPG, and the second car gets 15 MPG. The two cars combined drive a total of 1000 miles in that week, for a total gas consumption of 60 gallons. How many gallons were consumed by each of the cars that week.

and this is what I did:

x= First car @ 20MPG
y= Second car @ 15MPG

x+y=60
20x+15y=60
-20x -20x

15y=-20x+60
/15 /15 /15

y=-20/14x+4
y=-4/3x+4

20x+15(4/3x+4)=60
20x+20x+60=60
-60 -60
20x+20x=0
40x=0
/40 /40
x=40
y=20

2. Originally Posted by GeinoD
Is it ok if I ask another one?
of course it's ok. it would be a forum if it wasn't

Its a different type of question.

In a family there are two cars. In a given week, the first car gets an average of 20 MPG, and the second car gets 15 MPG. The two cars combined drive a total of 1000 miles in that week, for a total gas consumption of 60 gallons. How many gallons were consumed by each of the cars that week.

and this is what I did:

x= First car @ 20MPG
y= Second car @ 15MPG

x+y=60
20x+15y=60
-20x -20x

15y=-20x+60
/15 /15 /15

y=-20/14x+4
y=-4/3x+4

20x+15(4/3x+4)=60
20x+20x+60=60
-60 -60
20x+20x=0
40x=0
/40 /40
x=40
y=20

car x gets 20 MPG, so if it uses 40 gallons, it means it drove 20*40 = 800 miles

car y gets 15 MPG, so if it uses 20 gallons, it means it drove 15*20 = 300 miles

300 + 800 = 1100 miles. which is not what we are told they drove. so your solution can't be right.

let's start over...

Let $x$ be the number of gallons used by the 20 MPG car
Let $y$ be the number of gallons used by the 15 MPG car

clearly we have $x + y = 60$ .................(1)

(ah, you got that equation! nice job!)

also, for each gallon, car-x drives 20 miles, so the number of miles car-x drives is 20x, similarly, the number of miles car-y drives is 15y, since the cars drove a total of 1000 miles, we have

$20x + 15y = 1000$ ....................(2)

(aha! that's where you messed up)

now continue

3. ok, I got it

x+y=60

20x+15y=1000

x+y=60
-x -x
y=-x+60

20x+15(-x+60)=1000

20x-15x+900=1000
-900 -900
5x=100
/5 /5
x=20

20+y=60
-20 -20
y=40

x=20
y=40

4. Originally Posted by GeinoD
ok, I got it

x+y=60

20x+15y=1000

x+y=60
-x -x
y=-x+60

20x+15(-x+60)=1000

20x-15x+900=1000
-900 -900
5x=100
/5 /5
x=20

20+y=60
-20 -20
y=40

x=20
y=40
you got it, you're a genius!

5. Thank You very much for the help.
I am so thankful I found this site.