Problem Solving

In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4% sales tax to the dealer's price per gallon d, in dollars, 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

Answer to be posted later.

D) D = p - 0.18/1.04

I do not understand why it is -0.18 instead of +0.18. Can someone please explain?

The easiest way to start is to set up the equation in terms of d and p in the way the stimulus presents the question:

p = 1.04d + 0.18

Now solve for d:

p - 0.18 = 1.04d

d = (p - 0.18) / d

What a silly mistake it was... My formula was:

p + 0.18 = d + 0.04d when it should have been p = d + 0.04d +0.18.


Thanks grockit_jake!

Why is the answer not C?

If you assume gas costs $3.00 a gallon for the dealer (d), then you add tax and get $3.00 + $0.12 + 0.18 = $3.30 gallon (p)

Plugging into answer C

d = (p/1.04) - 0.18

$3.00 = ($3.30/$1.04) - $0.18
$3.00 = $3.17-$0.18
(close enough)

Trying a different price, the formula still holds.

$5.00 = ($5.38/$1.04) - $0.18

Close enough doesn't count. Sorry.

The reason it's so close is that 0.18 is really small relative to $5 or $3.

You have to "undo" the equation you put forward.

If you set d, then multiply by 1.04 and then subtract, to "undo" you must add first, then divide the sum.

Try answer C with $1 and see what you get

grockit_jake wrote:Close enough doesn't count. Sorry.

The reason it's so close is that 0.18 is really small relative to $5 or $3.

You have to "undo" the equation you put forward.

If you set d, then multiply by 1.04 and then subtract, to "undo" you must add first, then divide the sum.

Try answer C with $1 and see what you get

You are right. But try $3.00 with answer D and see what you get.

d = p - 0.18/1.04

$3.00 = [($3.00*1.04)+.18] - 0.18/1.04
3.00 = $3.30 - 0.17 does not equal $3.00

There's a typo on D in the original question that carlcat posted.

it should read.

D. d = (p - 0.18)/1.04

grockit_jake wrote:There's a typo on D in the original question that carlcat posted.

it should read.

D. d = (p - 0.18)/1.04

You are right for the typo, apologies.

I guess I'll take close enough, thanks.