Diana bought a stereo for $530, which was the retail price plus a 6

APPROACH #1: Algebra
Let x = the pre-tax price of the stereo Diana bought
Since the tax rate is 6%, the total taxes = 6% of x = 0.06x
So we can write: x + 0.06x = $530
Simplify: 1.06x = $530
Solve: x = 530/1.06 = $500

IF Diana had travelled to a neighboring state (with a 5% tax rate), the taxes would have equaled 5% of $500, which is $25
So, the total amount Diana would have paid = $500 + $25 = $525

$530 - $525 = $5
So, Diana would have saved $5.
Answer: D

APPROACH #2:Number sense

The question asks us to determine how much Diana would have saved if the sales tax were decreased 1% (from 6% to 5%)

Keep in mind that the $530 includes the price of the stereo AND the sales tax. So, taking 1% of $530 ($5.30) would be incorrect, because the stereo itself costs LESS THAN $530. So, the savings must be LESS THAN $5.30, which means we can eliminate answer choice E.

Now, those people who have real-life experience with 5% or 6% (or 8 or 9% even) sales tax know that the tax doesn't increase the final price by a whole lot. So, we should have a gut feeling that the price of the stereo is a little bit less than $530. How much less?

Well, without performing any calculations (i.e., using only your experience with 5% or 6% sales tax), do you think the pre-tax price of the stereo is $430? If so, then 1% of $430 = $4.30 in which case the correct answer is C

ORRRRRR, do you think the pre-tax price of the stereo is $500? If so, then 1% of $500 = $5.00 in which case the correct answer is D

Our experience and number sense should tell us that the pre-tax price of the stereo is a lot closer to $500 than to $430. So, the correct answer MUST be D

Cheers,
Brent
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Answer D
p+ tax = 106%
Price = 530/106 * 100 = 500
105% = 525
She will be saving 5 dollars. It just took me over two minutes, lame
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R=Retail Price

Store 1:

R(106/100)=530
R=(530*100)/(106) and recognize 106*5=530
Therefore R=500

Store 2:
500*(105/100)=5*105=$525

Savings=$530-$525=$5 (D)

Price at which Diana bought a stereo = 530$
Let the retail price = R
Percent of sales tax = 6%
R+.06R = 530
=>1.06R = 530
=> R = 500
Money spent in sales tax = 30$

In the neighboring state , she would have paid sales tax = 5%
Sales tax amount in neighboring state = (5/100)* 500 = 25 $
Diana could have saved = 30 - 25 = 5$

Answer D
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Let the retail price of the stereo be 100
Diana bought the stereo at 106



Price of the stereo in neighboring state is 105



Savings possible by buying the stereo from the neighboring state is 106 - 105 = 1



We know that when retail price is 106 , price of stereo is $530
When retail price is 1 , price of the stereo is 530/106 = $5

IMHO (D) $5.00
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We are first given that Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax, so we can create the following equation to determine S, the retail price of the stereo before sales tax:

Retail Price + Sales Tax = Total

S + .06S = 530

1.06(S) = 530

106(S) = 530 x 100

S = (530 x 100)/106 = (530 x 50)/53 = 10 x 50 = 500

(Note: Although the above equation appeared somewhat complicated, we see that through careful simplification, we can fairly easily come up with a final value of 500.)

We need to determine how much Diana would have saved had she purchased a $530 dollar stereo with a 5 percent sales tax rather than the stereo with a 6 percent sales tax. Thus, we are essentially determining the difference in the amount of tax paid and can determine this using the formula: Sales Tax = Retail Price x Tax Rate

The amount of sales tax, when paying 6%, is 500 x 0.06 = 30 dollars.

The amount of sales tax, when paying 5%, is 500 x 0.05 = 25 dollars.

Thus, the money saved when paying 5% is 30 - 25 = 5 dollars.

Answer: D
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To find the actual price of the item: 530/106*100=500
Adding 5% tax: 500/100*105= 525
To find the difference: 530-525=5

Can somebody refer to me a video on how to simplifiy 530/106 to 500?
what i am doing is
1% of 530 = 5.3
5.3*6= 31.8 ...
530-31.8= 498.2 ...

where am i making the mistake?

Hi JeevesAsk, 530/106 * 100 = 53000/106 = 500

Here you are calculating 1% of 530 = 5.3 ( which is the price with 6% already) when you should calculate with original price of 500 here.
so 1% of 500 = 5
5% of 500 = 5 * 5 = 25

530 - 525 = $5

Hope it make sense.