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 1550 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

About the same as the previous posting

a = gallons used up by the 20 mpg car

b = gallons used up by the 30 mpg car

we know on that week they both consumed 65 gallons altogether, therefore a + b = 65.

we also know that they did a combined mileage of 1550.  Now, in 1 gallon the 20mpg car does 20(1) miles, in 2 it does 20(2) miles, in 3 gallons it does 20(3) and in "a" it does 20(a) or 20a miles.

likewise, the 30mpg car does 30(b) in b gallons, or 30b miles.

Therefore, 20a + 30b = 1550.

$\bf \begin{cases} a+b=65\implies \boxed{b}=65-a\\ 20a+30b=1550\\ ----------\\ 20a+30\left(\boxed{65-a} \right)=1550 \end{cases} \\\\\\ 20a-30a+1950=1550\implies 400=10a\implies \cfrac{400}{10}=a\\\\\\ \stackrel{\textit{gallons}}{40}=a$

how many gallons is it consumed by the 30mpg car?  well b = 65 - a.