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Can someone explain this problem to me?? After a price reduction of x%, an item has its price increased to its original value. What was the percent of increase? Express your answer as a common fraction in terms of x.

User Ryber
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1 Answer

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Answer:


(-100(100+x))/((x-100))

Explanation:

Let the original price of the item = p

Let there was q% of increase on the original value, so

the printed price of the item,
C= p+p (q)/(100)=p(1+(q)/(100))

After a price reduction of x%, the has its price increased to its original value, so,


C-C* \frac {x}{100} = original price + increased price


p(1+(q)/(100))-p(1+(q)/(100))* \frac {x}{100} = p+p


(1+(q)/(100))-(1+(q)/(100))* (x)/(100) =2


-(1+(q)/(100))* (x)/(100) =2-1-(q)/(100)


-(1+(q)/(100))* (x)/(100) =1-(q)/(100)


(1+(q)/(100))* (x)/(100) =(q)/(100)-1


(x)/(100)+(q)/(100)*(x)/(100)-(q)/(100)=-1


x+x * (q)/(100)-q=-100


q((x)/(100)-1)=-100-x


q=(-100(100+x))/((x-100))

Hence, the percent of the increase is
(-100(100+x))/((x-100))

User Alp
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