Math Is Fun Forum

ineedhelp

Member

Registered: 2006-01-21

Posts: 7

a problem at work

I need help figuring out a percentage increase.  If, over 4 years the sales of all stores are listed below.  The sales at store 1 are to the right. 

Year     Sales at all stores      Sales at Store 1
2002      243                         11 (4.5%)
2003      192                         39 (20.5%)
2004      229                         59 (25.7%)
2005      253                         65 (25.8%)

What is the percentage increase each year?
What is the percentage increase from 02 to 05?
If the trend continues, what percentage increase can we expect in the next 3 years.

darthradius

Member

Registered: 2005-11-28

Posts: 97

Re: a problem at work

I'm not sure if I am answering your question correctly because I don't understand what the company-wide sales has to do with it...But based solely on your sales at Store 1:

In 2003, Store 1 made 354% of the previous year (254% increase), in 2004, a 51% increase and in 2005, a 10% increase...
So from 2002-05, it looks like a total increase of 491%...

But this is mainly due to the huge increases you saw in 2003.  It appears as though they are leveling off, but I do not really know how to predict what to expect in the next three years.  Probably 0-10% on the previous year.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
                                                             -Bertrand Russell

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: a problem at work

And there are different ways people may interpret the phrase "percentage increase".  Example:

2002      243                         11 (4.5%)
2003      192                         39 (20.5%)

Store 1's sales increased from 4.5% of the total to 20.5%, so it's percentage increase (of the total) was 20.5% - 4.5% = 16% (I have seem people look at it that way!)

But putting that aside, a percentage increase is normally: ((NewValue/OldValue) - 1) × 100 %

So, for example, Store 1 had an increase in the first year from 11 to 39, which is 39/11 = 3.55 times larger, or an increase of 2.55, or 255%.
Using the formula you get ((39/11) - 1) × 100 % = ((3.55) - 1) × 100 % = 2.55 × 100 % = 255%

If this is really a work-related question, then the "next 3 years" answer would be "depends on the business environment". It looks like Store 1 is peaking out, and could only expect modest growth, and that the whole business has had a downturn and is only now recovering. Based on the data you couldn't really say more than that

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: a problem at work

ineedhelp, I don't know who was doing the rounding for those colums up there.  The store one column appears to represent that store's percentage of all of the stores sales.

11/243(100) ≈ 4.53%
39/192(100) ≈ 20.31%
59/229(100) ≈ 25.76%
65/253(100) ≈ 25.69%

It appears that this trend (for percentage of company? sales) would have you returning near or even below the original percentage of total sales.

If you are however looking at just store 1 then;

C(a,b) = percent change(year 1 to year 2)

C(02,03) = (39-11)(100/11) ≈ 254.54%
C(03,04) = (59-39)(100/39) ≈ 51.28%
C(04,05) = (65-59)(100/59) ≈ 10.17%

C(02,05) = (65-11)(100/11) ≈ 490.91%

You can see by inspection that the percentage increases are about 1/5 of the previous year for the years we looked at.  So you can approximate these by;

C(05,06) ≈ 10.17/5% or 2.03%
C(06,07) ≈ 2.03/5% or .41%
C(07,08) ≈ .41/5% or .08%

So roughly, only a 2.5% increase in sales will occur over the next three years.

That's my interpretation of the numbers.

Last edited by irspow (2006-02-07 09:25:06)

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.