Math Percentage question. How do I get to it?

Question

Let's say have 100.00. let's say the price is 115.00 now. (115/110)-1 = .15 Therefore it is a 15% rate increase.

 

However, if i do 115 x .85  (100-15%)= its 97.75. why isnt it $100 given the percentage increase? How do i get it back to 100.00 in terms of percentage. what steps am i missing

Answer 1

Hi Kevin,

 

I'm going to try a real life problem but it may not answer all your questions.

 

Mary spent 100 dollars last week on food.  That went up 15% so she spent 115 this week.

 

John spent 115 dolllars last week on food.  That went down 15% and so he spent  97.75 this week.

 

Mary's increase is based on 15% of 100

John's decrease is based on 15% of 115  so his decrease is more than Mary's increaase

 

115 x (a change of 15%) is bigger than  100 x (a change of 15%)

 

Also if 100 increases 15% to go up to 115 then you can get back to your 100 by dividing by 1.15

 

I really hope this helps

 

Answer 2

 

You do 115 / 1.15 = 100

 

 

Proof:

   The original principal is X, and it was INCREASED BY 15% to GET 115.

   So

    115 = 100%*X +  15%*X = 115%* X  = 1.15X

 

X = 115/1.15 = 11500/115 = 100

Answer 3

when you do a percent of 115 you are doing that percentage of 100 but also the same percentage of the additional 15. if you want to get back the 100 you would need to do the following equation

 

115*x=100  x=100/115   0.870. if you multiply 115*.870=100  

 

a bit more than the .85 because you are also subtracting the percentage of the extra 15. (extra 15 of 115-100)