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.
Word Problem
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- grockit_jake
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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
p = 1.04d + 0.18
Now solve for d:
p - 0.18 = 1.04d
d = (p - 0.18) / d
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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
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
- grockit_jake
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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
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
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You are right. But try $3.00 with answer D 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
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
- grockit_jake
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There's a typo on D in the original question that carlcat posted.
it should read.
D. d = (p - 0.18)/1.04
it should read.
D. d = (p - 0.18)/1.04
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