MAT1033 word problem

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 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Let x = number of gallons used by the first car

 

Then, 45-x = number of gallons used by the other car

 

Then, 35x + 15(45-x) = 975

 

         35x + 675 -15x = 975

 

                         20x = 300

 

                            x = 15 gal

 

The first car used 15 gal while the second car used 30 gal.  

 

Answer 2

Let x = the gallons of gas used by car 1

 

y = the gallons of gas used by car 2

 

x + y = 45  (total amount of gas)

 

35x + 15y = 975 (number of miles traveled by the two cars)

 

Solve the first equation for y

 

y = 45 - x

 

Plug this into the second equation 

 

35x + 15(45 - x) = 975

35x + 675 - 15x = 975

20x + 675 = 975

20x = 300

x = 15

 

Car 1 used 15 gallons of gas, and car 2 used y = 45 - x = 45 - 15 = 30 gallons of gas