In a family there are two cars In a given week the first car

In a family there are two cars. In a given week, the first car gets an average of 30 miles per gallon, and the second car gets 40 miles per gallon. The two cars combined drive a total of 2500 miles in that week, for a total gas consumption of 70 gallons. How many gallons were consumed by each of the two cars that week?

Solution

x/30+(2,500-x)/40=70
(40x+30(2,500-x))/(30*40)=70
(40x+75,000-30x)/1,200=70
10x+75,000=70*1,200
10x+75,000=84,000
10x=84,000-75,000
10x=9,000
x=9,000/10
x=900 miles for the 30 mpg car.
2500-900=1,600 for the 40 mpg car.
Proof:
900/30+1,600/40=70
30+40=70
70=70