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 ans…

Question

asked Jan 3, 2021 34.4k views

1 Answer

Alp · Answer 1 · 2021-01-09T02:27:42+0000

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))