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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a
combined total of 1050 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?

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sqdancefan

Answer:

  • 30 mpg
  • 15 mpg

Step-by-step explanation:

Let x represent the fuel efficiency of one of the cars. Then 45-x is the fuel efficiency of the other. The total miles driven is then ...

  miles = (gallons)×(miles/gallon)

  20x +30(45-x) = 1050

  -10x +1350 = 1050 . . . simplify

  300 = 10x . . . . . . . . . . add 10x-1050

  x = 30 . . . . . . . . . . . . . divide by 10

  45-x = 45-30 = 15

The car using 20 gallons got 30 miles per gallon; the car using 30 gallons got 15 miles per gallon.

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