Solving a value mixture problem using a system of linear equations

Question

A family has two cars. The first car has a fuel efficiency of 15

 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 1575

 miles, for a total gas consumption of 65

 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Let a = # miles by car A and b = # miles by car B

a + b = 1575

a*(1/15) + b*(1/30) = 65

From the first equation, a = 1575 - b

Substitute into the second equation

(1575 - b)*(1/15) + b/30 = 65

Solve for b

105 - b/15 + b/30 = 65

-b/30 = -40

b = 1200

Then a = 1575 - 1200 = 375