In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
A) d= p-0.22
B) d= p/1.22
C) d= p/1.04 - 0.18
D) d= p-0.18 / 1.04
E) d= p-0.04 / 1.18
Dealer's cost:
Let d=1.
Selling price:
If d=1, then p = d + 4% tax + .18 = 1 + .04 + .18 = 1.22.
Since the problem asks for the value of d, our target is d=1.
Now we plug p=1.22 into the answers to which yields our target of d=1.
Only
D works:
d = (p - 0.18)/(1.04) = (1.22 - 0.18)/(1.04) = (1.04)/(1.04) = 1.
The correct answer is
D.
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