Question

A family has two cars. During one particular week, the first car consumed 35 gallons of gas and the second consumed

25 gallons of gas. The two cars drove a combined total of
2150 miles, and the sum of their fuel efficiencies was
70 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Answer 1

Call car one = o

Call car two = t

o = 35 gallons

t = 25 gallons

d1 = do

d2 = 2150 - do

effici_0 = e

effic_2 = 70 - e

35*e = do

25*(70 - e) = 2150 - do Substitute do into this equation

25*(70 - e) = 2150 - 35e Remove the brackets on the left

1750 - 25e = 2150 - 35e Add 35e to both sides

1750 - 25e + 35e = 2150 - 35e + 35e

1750 + 10e = 2150 Subtract 1750 from both sides.

1750 - 1750 + 10e = 2150 - 1750

10e = 400 Divide by 10

e = 40 Answer for Car 1

70 - e = effic2

70 - 40 = 30 Answer for Car 2