Complete question is;
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1850 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
Car 1 consumed 30 gallons of gas.
Car 2 consumed 20 gallons of gas.
Explanation:
Let x be number gallons consumed by car 1
Let y be number of gallons consumed by car 2
We are told that total gas consumption of 50 gallons. Thus;
x + y = 50 - - - - - eq(1)
We are told that the first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas and they went a combined total of 1850 miles. Thus;
35x + 40y = 1850 - - - - eq2
Let's make y the subject in eq(1),
y = 50 - x - - - - eq(3)
Putting 50 - x for y in eq 2 gives;
35x + 40(50-x) = 1850
35x + 2000 - 40x = 1850
-5x + 2000 = 1850
-5x = -150
x = 150/5
x = 30 gallons
Substitute 30 for x into eq 3,we have;
y = 50 - 30
y = 20 gallons
Thus;
Car 1 consumed 30 gallons of gas.
Car 2 consumed 20 gallons of gas.