Question

I have the following chart that I am supposed to find the percent increase in one step. The directions specifically say not to use a two step method.

10.5
12.5
14.9
17.7
21.1
25.1

So I divide 12.5 by 10.5, 14.9 by 12.5, etc.

When I do this (and round) I get about 19% increase for each one. (we are supposed to round. )

Then I have another chart that we are supposed to find the percent decrease also using the one step method.

80.2
71.4
63.5
56.5
50.3
44.8

If I use the same method I get about 12% decrease each time but the answer says 11% each time. If I do it the opposite way, for example, 71.4/80.2 and then subtract from 1.00 I would get more like 11%.

I'm just not really certain of the methodology to get the correct 11% answer.

Thank you

Answer 1

In the first one you divided the 2nd by the 1st and got
12.5/10.5 = 1.19.. = 1 + .19
= 100% + 19% ---> an increase (+) of 19%

I assume that is how you got 19%

So why not do the same thing in the 2nd ?

71.4/80.2 = .8902..
= 1 - .1097
= 100% - 10.97%
= 100% - 11.97% ---> a decrease (-) of appr 11%

I see no discrepancy in the methods

Notice we divided "in the same direction"

Answer 2

What I'm asking about is actually about the decrease in the second chart. If I divide top to bottom (80.2/71.4, 71.4/63.5, etc), I get a different result than if I divide bottom to top (71.4/80.2, 63.5/71.4 and then subtract from 1.00). If I do the top to bottom way I get 12% which I'm told is wrong. If I do bottom to top I get 11% which I'm told is correct. I just don't understand the WHY that is correct.

Answer 3

I thought I explained it quite simply.
Why would you change the "direction" of your division?
I consistently divided the old one from the new one (2nd - 1st)

if the result is greater than 1 you have an increase, and the increase is the difference between 1 or 100% and your answer.

if the result is less than 1 you have a decrease, and the decrease is the difference between 1 and your answer.

I did the same thing in both cases.

in the first you correctly divided 12.5 by 10.5
but for the second you changed it to 80.2/71.4 . Why would you switch???
and not do the same as in the first question?

Answer 4

I apologize for asking for clarification because I did not understand.