Percentages and Applied Problems

[britney89]

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

I have the same process, but the percentage being multiplied by the price is different, the answer has the equation to be 530=1.06r, I'm just wondering how/why the percentage multiplied by the retail price is 1.06 and not 0.06?

Thanks!!

[Anurag@Gurome]

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

Say the retail price is R%

Hence, price of the stereo = Retail price + 6% tax on the retail price = R + 6% of R = R + 0.06R = 1.06R

Now, 1.06R = 530 ---> R = 500

Price of the stereo in the neighboring state = 1.05R = $525

Hence, she could have saved $(530 - 525) = $5

[factor26]

i used to be confused on this topic too!

just think of it this way ... if i gave you $100 to invest in a bond whose yield is 6% (dont worry about compounding now ) when i ask you how much will you have at the end of the year you can say

orig inv = $100.00
6% return $6.00
Total = $106.00

other ways to look at this

x = orig inv

x + .06x = answer

combine terms ...

1.06x = answer ... i used to solve at first by using the x + .06x equation ... but in an effort to save time i adapted and used the 1.06x equation ... saves me a step in the calculation which is really meaningful when taking the gmat considering it is a timed test!!

[fcabanski]

Whenever you see problems like this, including work problems and d=rt problems, write down the general formula, and then a formula for each situation - there are usually 2, but sometimes 3.

Identify the problem type. Set up your solution. Make sure you know what is being asked, and that you've set up correctly. Execute.

Identify - Sale Price, original price, sales tax problem.

General formula: P=(1+r)*C


Situation 1: 530=(1.06)*C
Situation 2: P = (1.05)*C

Make sure - the problem asks to find what she could have saved, so P (from situation 1) which is 530 - P (situation 2).

Note situation one contains only one variable. Note situation two can be solved if C is known. Situation one can provide C.

Do the math.

530/1.06=C=500

Sit. 2: P = (1.05)*500=525

Answer: 530-525= 5

[Abhishek009]

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

I have the same process, but the percentage being multiplied by the price is different, the answer has the equation to be 530=1.06r, I'm just wondering how/why the percentage multiplied by the retail price is 1.06 and not 0.06?

Thanks!!

Let the price of the stereo be 100

Sales tax is 6

So, price after sales tax is 106


Now 106 represents 530

so 100 represents (530/106)*100

So, Actual price of the stereo is $500



Sales tax in the other state is 5%

So price of the stereo after the tax is 500 * 105/100 => $ 525




So total savings is $ 5




Coming to your query -


let the price of the stereo be 100

Tax is 6% => 6

So price after the tax is 106



Hence the multiplicand is 1.06 not 0.6!!!!

[fcabanski]

The formula is

P = (1=r) * C

Where C is the cost before tax, and P is the final price and r is the sales tax.

Another way to write this is:

P = C +rC

Price is the cost plus the sales tax rate times the cost. rC is the sales tax in dollars.