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Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $\$ 5$. Assuming gasoline costs $\$ 4$ per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?

SAT · Math · previous-year question

  1. A.$\frac{25}{4} m=95$
  2. B.$\frac{25}{4} m=5$
  3. C.$\frac{4}{25} m=95$
  4. D.$\frac{4}{25} m=5$correct

Answer

D. $\frac{4}{25} m=5$

Explanation

Choice D is correct. Since gasoline costs $\$ 4$ per gallon, and since Alan's car travels an average of 25 miles per gallon, the expression $\frac{4}{25}$ gives the cost, in dollars per mile, to drive the car.Multiplying $\frac{4}{25}$ by $m$ gives the cost for Alan to drive $m$ miles in his car. Alan wants to reduce his weekly spending by $\$ 5$, so setting $\frac{4}{25} m$ equal to 5 gives the number of miles, $m$, by which he must reduce his driving.Choices $A, B$, and $C$ are incorrect. Choices $A$ and $B$ transpose the numerator and the denominator in the fraction. The fraction $\frac{25}

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