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Connie paid a sales tax of 8 percent on her purchase. If the sales tax

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RyanDe680
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Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   Updated on: 16 Aug 2015, 10:15
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Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A. $368
B. $380
C. $400
D. $420
E. $432
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E

Originally posted by RyanDe680 on 09 May 2008, 18:58.
Last edited by Bunuel on 16 Aug 2015, 10:15, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   09 May 2008, 19:00
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E

3% = $12
1% = $4

100% = $400

8% = $32

400 + 32 = 432
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Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   Updated on: 17 Dec 2020, 00:55
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RyanDe680 wrote:
Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A) $368

B) $380

C) $400

D) $420

E) $432



Let, The Price of the \(= x\)

so,
\(1.08x - 1.05x = 12\)

\(0.03x = 12\)

\(x = 400\)

The Price \(= $400\)

Sales tax \(400*8\)%\( = 32\)

The Connie actually Paid \(= 400+32= $432\)

The answer is \(E\)

Originally posted by MHIKER on 04 Dec 2011, 11:43.
Last edited by MHIKER on 17 Dec 2020, 00:55, edited 3 times in total.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   09 May 2008, 19:03
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P*1.08=T1
P*1.05=T2=T1-12

combine eqns
p(.03)=12
12/.03=400

400*1.08=432
E
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   05 Dec 2011, 09:04
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Hi Baten, I did your way. But I only subtracted and not added. the shortcut shown is great. But I am not sure if % can be worked that ways always.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   06 Dec 2016, 21:04
0.08P=C
0.05P=C-12

0.05P=0.08P-12
12=0.03P
P=400

0.05x400=32

400+32=432

E.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   14 Jul 2018, 05:36
First we need to make a valid equation. Let's assign the constant sale price with a variable x. We should bring two cases -- case 1st with the 8% and case 2nd with the 5% into equilibrium. So we have x+x(0.08) =x+x(0.05)+12. We need to add 12 to the 2nd case to maintain the equation. After solving the equation, we get that x equals to 400. But be CAREFUL and do not jump into the answer choices. I will advise everyone to reread the problem after relatively completing it. In the last step, we need to add 32 (which is the 8% of the 400) to 400 to get the satisfying answer.
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Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   Updated on: 13 Nov 2019, 07:40
\(x+\frac{(2x)}{25}=A\)

\(x+(\frac{x}{20})=A-12\)

\(x+\frac{(2x)}{25}=432\)

EDIT (13/11/2019): Even easier way

\(\frac{3}{100}x=12 \implies x+\frac{8}{100}x=432\)

Originally posted by SchruteDwight on 21 Aug 2019, 03:08.
Last edited by SchruteDwight on 13 Nov 2019, 07:40, edited 3 times in total.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   23 Aug 2019, 11:41
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RyanDe680 wrote:
Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A. $368
B. $380
C. $400
D. $420
E. $432


Let’s let n = the selling price of the item before tax. Thus, the total sales tax with a tax rate of 8 percent would be 0.08n, and the sales tax with a tax rate of 5 percent would be 0.05n. We are given that the difference in the two sales tax amounts is $12. Thus, we can create the equation:

0.08n - 0.05n = 12

0.03n = 12

n = 400

So the total amount paid was 1.08 x 400 = 432 dollars.

Answer: E
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Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   07 Nov 2021, 03:53
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Sales-------------Tax------------------Sales and Tax
x---------------- 0.08x------------------1.08x
x---------------- 0.05x------------------1.05x
1.08x - 1.05x = 12
=> x = 400
=> Total = 1.08x 400 = 400+400x 0.08= 432
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   14 Nov 2021, 07:46
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RyanDe680 wrote:
Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A. $368
B. $380
C. $400
D. $420
E. $432


Let's start with the following word equation: (total cost including 8% tax) - (total cost including 5% tax) = $12

Let x = the cost of the purchase (without tax)

So we can write: (x + 8% of x) - (x + 5% of x) = $12
In other words: (x + 0.08x) - (x + 0.05x) = $12
Simplify: 0.03x = 12
Solve: x = 12/0.03 = 1200/3 = 400

So, the cost of the purchase (without tax) is $400

So, the total amount Connie paid = $400 + (8% of $400) = $432

Answer: E
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   24 Dec 2021, 00:38
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Let the Selling price of the product = S.P

Amount paid including the sales tax of 8 % = 108% of SP

It's given that if the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase.

i.e 108 % of SP - 105% of SP = 12

3% of SP = 12

We need to find amount paid including the sales tax i.e 108 % of SP = \(\frac{12}{3} * 108\) = 432 $

Option D is the answer.

Thanks,
Clifin J Francis.
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   10 Jul 2022, 01:23
My 2 cents on this:

I equated as follows:

Total purchase = x

0.05x = 0.08x - 12

x = 400.

Question asks for total purchase cost + sales tax, so 400 + 8% of 400 = 432
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink] New post   19 Jan 2024, 19:24
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Re: Connie paid a sales tax of 8 percent on her purchase. If the sales tax [#permalink]
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