How do I calculate percentage increase?

Question

What is the formula for percetage increase? For example I'm trying to calulate the origional number. Number is $108.90, it increase 8.9%, how do I get back to the origonal number which is $100? What is this formula.

Or once again. Number is $136.13, increase 8.9% how do I get back to $125?

How do I know going backwards what the old number was after increasing 8.9%

Thanks!

Answer 1

If you want to increase something by a certain percent, what you do is multiply the original by (100% + increase%)

For example, for a 8.9% increase, you would multiply the original $125 by 108.9%
new = old * (100+x)%, where x is the increased percent
new = 125 * 1.089
new = 136.13

So to go backwards, you would divide by the same total percent increase.
old = new / (100+x)%
old = 136.13 / 1.089
old = 125

Answer 2

Formula is :
Original Number = [N x 100] / (100 + p)
where N = increased number,
p = percentage increase.
Examples :
(1) N = $108.90, p = 8.9 then
Original Number = [$108.90 x 100] /
(100 + 8.9)
= $10890 / 108.90
= $100.00
(2) N = 136.13, p = 8.9 then
Original Number = [$136.13 x 100] /
(100 + 8.9)
= $13613 / 108.90
= $ 125.00

Answer 3

divide the percent increase by 100

8.9/100 = .089

The algebraic formula is then

x + .089x = 108.9

1.089x = 108.9
divide both sides by 1.089

x = 100

The formula will hold for all cases of percent increase to find the original number.

x + .089x = 136.13
1.089x = 136.13
x = 125.00

Answer 4

1st question:
= $108.90 / (1 + 8.9%)
= $108.90 / (1 + 0.089)
= $108.90 / 1.089
= $100.00

2nd question: The exact original amount is $136.125 instead of $136.13 which was already rounded by dropping 0.005 and increasing the cents by 0.01 from 0.12 to 0.13.
= $136.125 / (1 + 8.9%)
= $136.125 / (1 + 0.089)
= $136.125 / 1.089
= $125.00

Answer 5

original number = new number / (1 + %/100)

example:
original no. = 136.13 / (1+8.9/100)
= 136.13 / (1+0.089)
= 136.13 / 1.089
= 125.00

Answer 6

Question 1
108.9%<---->$108.90
100%<--->(100 / 108.9) x $108.90 = $100

Question 2
108.9%<---->$136.13
100%<--->(100/108.9) x $136.13 = $125