In a family there are 2 cars in a given week the first car g

In a family there are 2 cars in a given week, the first car gets a average of 40 miles per gallon, and the second car gets 30 miles per gallon. the two cars combined drive a total of 1800 miles in that week, for a total gas consumption of 55 gallons. how many gallons were consumed by each of the two cars that week?

Solution

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