A person gets a 10% raise. After two weeks, the boss decides that the person does not deserve the raise. By what percent does the boss have to decrease the person's salary to return it to the original amount? Show your work. (N.B.: I realize through estimation that the percentage is less than 10% but I don't know how to arrive at the correct answer. Thanks.)

Question

A person gets a 10% raise.  After two weeks, the boss decides that the person does not deserve the raise.  By what percent does the boss have to decrease the person's salary to return it to the original amount?  Show your work.  (N.B.:  I realize through estimation that the percentage is less than 10% but I don't know how to arrive at the correct answer.  Thanks.)

lukecrayonz · Answer

10%...?

lukecrayonz · Answer

Salary beginning 10,000
Raise by 10%
11,000
Deduct 10%, 1,100
10,000

lukecrayonz · Answer

Am I skipping something or is this just extremely obvious?

anonymous · Answer

If you deduct 10% from 11,000 you will not get the original $10,000.  Ten percent of $11,000 is $1,100 so, yes, you are missing something.

anonymous · Answer

It's approximately 9.1%. More precisely 9.09%.

anonymous · Answer

Gezimbasha, how do you arrive at the 9.09%.  I need to be able to work this kind of problem.  Faleminderet.

anonymous · Answer

Ooh, nice. Here. You know that after the raise, you have $11,000. So now you need to subtract a percentage of that and you need it to equal 1000.$$11,000-\frac{x}{100}*11,000=10,000$$Now, just solve for x. First move the 11,000 on the right side.$$-\frac{x}{100}11,000=10,000-11,000=-1000$$Multiply by (-1) to get positive on both sides. And then divide by 11,000.$$\frac{x}{100}=\frac{1000}{11,000}=0.0909$$Multiply by 100. And you have,$$x=0.0909*100=9.09091$$
Proof:
$$11,000 - \frac{9.09091}{100}*11,000=10,000$$Je i mireseardhur!

anonymous · Answer

Gezim, the original question doesn't give an amount of $10,000.  Someone who answered the questions incorrectly put in the amount of $10,000 as the base salary.  If we don't know the base salary but only that it was raised by ten percent and then lowered back to the original amount.  How do I write the equation to come up with the same answer you have given.  Faleminderet.

anonymous · Answer

Assume that the base salary is x. Now the increased salary is y. Therefore we have,$$x+0.1x=y$$Where 0.1=10%. Now we want to get back to the same base salary. We form the equation as I said.$$y-z y=x$$Where z is the percentage of decrease. Now, we factor one y, and we get this equation.$$y(1-z)=x$$We know that y=(x+0.1x) so we replace that,$$(x+0.1x)(1-z)=x$$Divide by x and you get$$(1+0.1)(1-z)=1$$Do the math there, and you get$$1.1-1.1z=1$$Subtract 1.1 and then multiply by (-1) to get positive. $$z=\frac{0.1}{1.1}$$From which you get. Ultimately you will get, z=0.0909. When you multiply by 100% to get it in percentage, you get 9.09%. :)

anonymous · Answer

Faleminderet!!!!  Kuptoj!!!