7th grade proportions problem

[silkroadtomandarin]

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.

 

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In particular, what have you thought about or tried thus far in this exercise? Have you learned about percents? Do you know what it means to increase a value by 10%?

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[HallsofIvy]

You form a percentage change by dividing the actual change by the "base"- the original value. Suppose the persons original salary was "S". If we call the raise "R", then saying it was a 10% raise means $\displaystyle \frac{R}{S}= .10$ so that R= .10S and the new salary is S+ .10S= (1.1)S. When we talk about a new raise or reduction, we have to use that new salary as base. If we want to reduce back from (1.1)S to S, we have to reduce by .1S, the same amount we raised by before. But the base has changed. The percentage reduction is $\displaystyle \frac{.1S}{1.1S}= \frac{.1}{1.1}$ since the "S"s cancel.