Using a system of linear equations

Question

Problem Page
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
40
miles per gallon of gas. During one particular week, the two cars went a combined total of
2000
miles, for a total gas consumption of
75
gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Suppose the first car (low efficiency) consumed X gallons, the second car (high efficiency) consumed Y gallons.

 

The total gas consumption is 75 gallons, so it means: X + Y = 75

 

The first car has a fuel efficiency is 15 miles/gallon, X gallons ran 15 X miles.

The second car has a fuel efficiency is 40 miles/gallon, Y gallons ran 40 Y miles.

The combined total mileage is 2000 miles. So, we can set up the second equation for the total mileage: 15 X + 40 Y = 2000

 

X + Y = 75 (total gallons of gas consumed)

15 X + 40 Y = 2000 (total mileage)

 

15 X + 15 Y= 1125 (the first equation both sides multiply 15)

 

25 Y = 875 (two equations subtract)

 

Y = 35 (gallons)

 

X + Y = 75 

X + 35 = 75 (substitution)

X = 40 (gallons)

 

On that week,

The first car consumed 40 gallons, the second car consumed 35 gallons.