In a certain state, gasoline stations compute the price per gallon \(p,\) in dollars, charged at the pump by adding a

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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. \(d=\dfrac{p}{1.22}\)

C. \(d=\dfrac{p}{1.04}-0.18\)

D. \(d=\dfrac{p-0.18}{1.04}\)

E. \(d=\dfrac{p-0.04}{1.18}\)

Answer: D

Source: Official Guide

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VJesus12 wrote:
Fri Feb 19, 2021 7:11 am
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. \(d=\dfrac{p}{1.22}\)

C. \(d=\dfrac{p}{1.04}-0.18\)

D. \(d=\dfrac{p-0.18}{1.04}\)

E. \(d=\dfrac{p-0.04}{1.18}\)

Answer: D

Source: Official Guide
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 . . .
We can write: p = d + 4% of d
= d + 0.04d
= 1.04d
So, we have: p = 1.04d

. . . and then adding a gasoline tax of $0.18 per gallon.
We get: p = 1.04d + 0.18

Which of the following gives the dealer's price per gallon "d" in terms of the price per gallon "p" charged at the pump?
We need to take p = 1.04d + 0.18 and solve for d

Take: p = 1.04d + 0.18
Subtract 0.18 from both sides to get: p - 0.18 = 1.04d
Divide both sides by 1.04 to get: (p - 0.18)/1.04 = d

Answer: D
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