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A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 2125 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?

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chikafujiwara

Answer:

Car 1 : 40 gallons

Car 2 : 15 gallons

Step-by-step explanation:

F = Car 1 Fuel Efficiency

S = Car 2 Fuel Efficiency

F + S = 55

40F + 35S = 2125

Using the first equation...

S = 55 - F

Then substitute into the second equation.

40F + 35(55 - F) = 2125

Simplify

40F + 1925 - 35F = 2125

5F + 1925 = 2125

5F = 200

F = 40

Then plug it back into S = 55 - F

S = 15

Plug it back into F + S = 55 to check.

Hope this helps.

Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

Let car 1 fuel efficiency = x

Let car 2 fuel efficiency = y.

Based on the information given,

x+ y = 55 ...... i

40x + 35y = 2125 ...... ii

Therefore, y = 55 - x ..... iii

Put equation iii into ii

40x + 35(55 - x) = 2125

40x + 1925 - 35x = 2125

Collect like terms

40x - 35x = 2125 - 1925

5x = 200

x = 200/5

x = 40

Since x + y = 55.

y = 55 - 40 = 15

Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

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