A family has two cars. The first car has a fuel efficiency of 40 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 1025 miles, for a total gas consumption of 35 gallons. 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 40 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 1025 miles, for a total gas consumption of 35  gallons. How many gallons were consumed by each of the two cars that week?

anonymous · Answer

x = car with 40 mph gas
y = car with 15 mph gas

x + y = 35 --> x = 35 - y
40x + 15y = 1025

now sub 35 - y in for x in the 2nd equation
40x + 15y = 1025
40(35 - y) + 15y = 1025
1400 - 40y + 15y = 1025
1400 - 25y = 1025
-25y = 1025 - 1400
-25y = - 375
y = -375/-25
y = 15

now sub 15 in for y in the 1st equation
x + y = 35
x + 15 = 35
x = 35 - 15
x = 20

check...
40x + 15y = 1025
40(20) + 15(15) = 1025
800 + 225 = 1025
1025 = 1025

the 40 mph (x) uses 20 gallons
the 15 mph car uses 15 gallons

anonymous · Answer

any questions ?