Result of an increased % when ONLY the result of the OLD % is known

[mhazaa]

Hi (first time post)

I got this from a bank of questions that leads me to believe this SHOULD be easy- but the solution is not coming to me:

The tax rate for businesses was increased by half of 1%. If a business was paying 20 000 dollars in taxes before the increase, how much would the business pay after the increase?

(I know it's not a direct function of the 20 000 dollars)

Thanks!

 

[MarkFL]

Hello and welcome to MHB, mhazaa! :D

It seems we need another piece of information here...are you given either the initial tax rate or the amount on which the business is being taxed?

 

[mhazaa]

Hi - thanks for responding

That was my initial thought, but no, that's it! I copied the question verbatum.

(It's from a high school textbook!)

 

[MarkFL]

Let's take a look at two different scenarios in which the tax amount is 20 (in thousands of dollars).

Case 1:

Taxed amount: 2000
Tax rate: 1%

Case 2:

Taxed amount: 1000
Tax rate: 2%

In case 1, if we increase the tax rate to 1.5%, then the increase in tax is 10. But, in case 2, if we increase the tax rate to 2.5%, then the increase in tax is 5. So, we see that the change in tax is a function of the taxed amount $A$. We in fact find that the new tax amount $T$ would be given by:

\(\displaystyle T=20+0.005A\)

So, without knowing the taxed amount either directly, or by inferring it from knowing the initial tax rate, we cannot give a unique solution to this problem. :D

 

[mhazaa]

:)

I approached it the exact same way (and came to the conclusion that *I* couldn't do it... But my level of math/math confidence didn't allow me to conclude that "it" couldn't be done!

I'm actually pleased to have the confirmation!

Thanks.

(now... watch somebody do it!)