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

Question

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 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1925 miles, for a total gas consumption of 60 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Let x = #gallons consumed by car that gets 30 miles to every gallon

y = #gallons consumed by car that gets 35 miles to the gallon

That means the following:

30x represents the number of miles travelled by car x

35y represents the number of miles travelled by car y.

Come up with two equations that model the situation:

x + y = 60 [ total gallons consumed was 60]

30x + 35y = 1925 [ total distance travelled by both cars]

How to solve that system? There are 5 or so techniques for solving a system of linear equations with two unknowns, two of which are substitution and addition/elimination. When it is straightforward to isolate one of the variables, substitution is usually a good choice.

Solve the first equation for y in terms of x by subtracting x from both sides:

y = 60 - x

Substitute 60 - x for y in the 2nd equation. This allows you to solve for x.

30x + 35(60 - x) = 1925

30x + 35(60) - 35x = 1925 [ distribute the 35, note, at this point you could also determine the value of 35(60) -- 2100]

-5x = 1925 - 35(60) [combine similar terms and subtract 35(60) from both sides or -175]

x = [1925 - 35(60)] / - 5 [divide both sides by - 5 (-175 / -5 = 35)]

x = -385 + 420 = 35 gallons

y = 60 - 35 = 25 gallons [ use y = 60 - x to find y]

Check:

35 gal (30 miles/gal) = 1050 miles

25 gal (35 miles/gal) = 875 miles

1050 + 875 = 1925 miles