Dealing with a percentage problem

[AleksandrM]

I am getting so frustrated with this reocurring dilemma.

The following problem is from OG PS.

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

I know the set-up x + .06x = 530
1.06x = 530
x = 530/1.06

This is the part that is my personal dilemma. How to divide this last part? I cannot come up with a useful shortcut. Also, this is not exactly a problem that you can eyeball the answer for. Because you need the exact amount, then calculate by .05, then subtract and get the exact savings.

[rajmirra]

OK. Here is how I would solve this problem.

If 106% is 530 what is 105%?

(530/106)*105= (5/1)*105= 525

The difference is 530-525 which is $5.

Hope this helps a bit!

~R

[aarunibens]

Problems where calculators are not allowed usually are in forms of multiples of numerator or the denominator. If not then you quickly have to guess, how many times is the numerator of the denominator or vice-versa. It is then easier to get close to the answer.

In this case 106 is 2 times 53.

[neobaby]

its basically 530/1.06 = (530/106)*100
This makes things simple as 530/106 =5

5*100 = 500

hope this helps

[yev23]

It's actually simple to calculate 530/1.06 if one realizes that 530 = 5*106 (or 5*100 + 5*6). 5% of 500 is even easier: 5% of 100 is 5, so 5*5 = 25. So you've got 530-525 = 5.