Explanation
Correct answer: D.
Choice D is correct. Since gasoline costs $ per gallon, and since Alan's car travels an average of miles per gallon, the expression gives the cost, in dollars per mile, to drive the car. Multiplying by gives the cost for Alan to drive miles in his car. Alan wants to reduce his weekly spending by $, so setting equal to gives the number of miles, , by which he must reduce his driving.
Desmos solution:
Note: Each mile costs 4/25 dollars in gasoline, so the weekly reduction m saves 5 dollars.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. This choice transposes the numerator and the denominator in the fraction. The fraction would result in the unit miles per dollar, but the question requires a unit of dollars per mile. Additionally, this choice sets the expression equal to instead of , a mistake that may result from a misconception that Alan wants to reduce his driving by miles each week; instead, the question says he wants to reduce his weekly expenditure by $.
Choice B
Choice B is incorrect. This choice transposes the numerator and the denominator in the fraction. The fraction would result in the unit miles per dollar, but the question requires a unit of dollars per mile.
Choice C
Choice C is incorrect. This choice sets the expression equal to instead of , a mistake that may result from a misconception that Alan wants to reduce his driving by miles each week; instead, the question says he wants to reduce his weekly expenditure by $.