Percentage change help please

[Shoppingal]

What was the percentage change in unit price when the regular size of Dove soap bars dropped from 100g to 90g (with no change in the price per bar)?

Vf-Vi x100% = 90g-100g x100% = -10%
Vi 100

The answer given is 11.11% can you tell me what I did wrong.
Thanks for any help provided.

 

[soroban]

Hello, Shoppingal!

What was the percentage change in unit price when the regular size of Dove soap bars
dropped from 100g to 90g (with no change in the price per bar)?

Think about what just happened . . .


We get less soap for the same price.
. . We will be paying more for each gram of soap.
. . We should expect a positive answer.


Suppose the original price for a Dover bar was \(\displaystyle P\) dollars.
. . The original unit price was: .\(\displaystyle \frac{P}{100}\) dollars/gram.

Now we pay \(\displaystyle P\) dollars for only \(\displaystyle 90\) grams of soap.
. . The new unit price is: .\(\displaystyle \frac{P}{90}\) dollars/gram.

The change in the unit price is: .\(\displaystyle \dfrac{P}{90} - \dfrac{P}{100} \:=\:\dfrac{P}{900}\) dollars/gram.


The percentage of change is: .\(\displaystyle \dfrac{\text{change in unit price}}{\text{original unit price}}\)

Therefore: .\(\displaystyle \dfrac{\frac{P}{900}}{\frac{P}{100}} \;=\; \dfrac{1}{9} \;=\;11\frac{1}{9}\%\)

 

[Shoppingal]

Thank you both for your help I understand where I went wrong. It's nice to have some help.