SOLUTION: A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 1650 m

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Question 1165931: A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 1650 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
miles divided by gallons = miles per gallon.

let x = the miles driven by the car that consumed 30 gallons of gas.

let y = the miles driven by the car that consumed 35 gallons of gax.

total miles driven is 1650.

your two equations are:

x + y = 1650
x/30 + y/35 = 50

the first equation tells you the total miles driven.
the second equation tells you the total miles per gallon consumed.

multiply both sides of the first eqution by 30 and multiply both sides of the second equation by 30 * 35 = 1050 to get:

30x + 30y = 49500
35x + 30y = 52500

subtract the first equation from the second to get:
5x = 3000

solve for x to get:
x = 600

since x + y = 1650, this makes y = 1050

you have x = 600 and y = 1050

check to see if these values make your original equations true.

your original equations are:
x + y = 1650
x/30 + y/35 = 50

these equations become:
600 + 1050 = 1650 which is true.
600/30 + 1050/35 = 50 which is also true.

miles / gallons = miles per gallon.

600/30 = 20 miles per gallon for the car that consumed 30 gallons.
1050/35 = 30 miles per gallon for the car that consumed 35 gallons.

those are your solutions.

to double check:

miles / miles per gallon = gallons consumed.

600/20 = 30 gallons
1050 / 30 = 35 gallons

it all checks out.

your solution is that the first car had a fuel efficiency of 20 miles per gallon and the second car has a fuel efficienty of 30 miles per gallon.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
              Fuel Effic.     Volume          DISTANCE

firstcar       x              30              30x

secondcar      y              35              35y

totals        50                             1650

system%28x%2By=50%2C3x%2B3.5y=165%29-----------solve system in any way you want.


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system%283x%2B3y=150%2C3x%2B3.5y=165%29

EQ2-EQ1:
0.5y=15
y=15%2A2
highlight%28y=30%29-------------simple arithmetic will give highlight%28x=20%29