A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas.

Question

A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1300 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

x+y=50        

 

20x+30y=1300

 

 

Substitute 

 

y=50-x  (1st equation) into 2nd equation to get

 

20x +30(50-x)=1300

20x  +1500-30x=1300

x=-200/-10=20

 

Answer x=20 gallons

x+y=50

20+y=50

y=30 gallons

 

check your answer

20x +30y = 1300

20(20) + 30(30)= 1300

400+900=1300  checks out correct