Problem Solving

EricKryk wrote:Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax. How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state where she would have paid a sales tax of 5 percent?

A) $1.00
B) $2.65
C) $4.30
D) $5.00
E) $5.30

Another approach is to apply a bit of 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

EricKryk wrote:Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax. How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state where she would have paid a sales tax of 5 percent?

A) $1.00

B) $2.65

C) $4.30

D) $5.00

E) $5.30

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