Question 161050
Let x=number of gallons consumed by the 40 mpg car
And let y=number of gallons consumed by the 30 mpg car
Now we are told that x+y=55---------------------------------eq1
Now we know that distance travelled by the 40 mpg car =40x
And the distance travelled by the 30 mpg car =30y
And we are also told that:
40x+30y=1800--------------------------------------------------eq2
 divide each term of eq2 by 10 just to reduce the size of the numbers
4x+3y=180------------------------------------eq2
 multiply eq1 by 4 (and we get4x+4y=220) and then subtract if from eq2:
-y=-40 divide each side by -1
y=40--------------number of gallons consumed by the 30 mpg car
 substitute y=40 into eq1:
x+40=55 subtract 40 from each side
x=15 -------------------number of gallons consumed by the 40 mpg car

CK
30*40+40*15=1800
1200+600=1800
1800=1800

Hope this helps---ptaylor