1. ## Product splitting

Hi guys, I need some help with a problem that seems quite easy but I have struggled with so far. I have the total sales of a product for 5 years. I have the % growth by year for each of the 5 products that combine the total and i need to find the %split of the total, by product. So far i tried solving by simultaneous equations but these seem to give negative numbers. Possibly because the source data is inaccurate. I wondered if this was the best way or if there were any way to estimate the splits?

2006 2007 2008 2009 2010
a 23.3% 19.1% 6.2% 10.5% 20.8%
b 14.0% 14.7% 24.5% 0.5% 8.6%
c 12.0% 8.7% 10.4% 10.0% -2.3%
d 26.3% 18.0% 2.9% 2.9% 15.0%
e 4.4% 13.7% 13.2% 0.2% 4.8%
total 9369 10827 12383 12524 13876

The table above shows the percentage increase of each product (a-e) from the previous year and the total sales of a-e for that year. I need to know the split of a-e in making up the total for each year. Ideas?

Apologies if this is in the wrong section and thanks in advance.

2. Hello, abc434589!

I have the total sales of a product for 5 years.
I have the % growth by year for each of the 5 products that combine the total
and i need to find the %split of the total, by product.
i tried solving by simultaneous equations but these seem to give negative numbers.
Possibly because the source data is inaccurate.
I wondered if this was the best way or if there were any way to estimate the splits?

$\displaystyle \begin{array}{c|ccccc|} \text{Product} & 2006 & 2007 & 2008 & 2009 & 2010 \\ \hline a & 23.3\% & 19.1\% & 6.2\% & 10.5\% & 20.8\% \\ b & 14.0\% & 14.7\% & 24.5\% & 0.5\% & 8.6\% \\ c & 12.0\% & 8.7\% & 10.4\% & 10.0\% & \text{-}2.3\% \\ d & 26.3\% & 18.0\% & 2.9\% & 2.9\% & 15.0\% \\ e & 4.4\% & 13.7\% & 13.2\% & 0.2\% & 4.8\% \\ \hline \text{Total} & 9369 & 10827 & 12383 & 12524 & 13876 \\ \hline \end{array}$

The table above shows the percentage increase of each product (a-e)
from the previous year, and the total sales of a-e for that year.
I need to know the split of a-e in making up the total for each year. Ideas?

I'm not familiar with the term %split.
Would you explain it . . . or give us the original wording of the problem?

I see a lot of messy algebra/arithmetic in our future.

$\displaystyle \text{Suppose product }a\text{ sold }A\text{ units in 2005.}$
$\displaystyle \text{Then in 2006, they sold: }\,1.233A\text{ units.}$
$\displaystyle \text{Then in 2007, they sold: }\,(1.191)(1.233A)\text{ units.}$
$\displaystyle \text{Then in 2008, they sold: }\,(1.062)(1.191)(1.233A)\text{ units.}$
$\displaystyle \text{Then in 2009, they sold: }\,(1.105)(1.062)(1.191)(1.233A)\text{ units.}$
$\displaystyle \text{Then in 2010, they sold: }\,(1.208)(1.105)(1.062)(1.191)(1.233A)\text{ units.}$

Do the same for all five products and revise the chart.
Add down the columns and create a system of five equations.
Solve the system and determine the original number of each product.

Good luck!

3. Thanks Soroban, that is how i originally solved it, however I get a-e to be:

27361.08 a -28734.6
b -17959.4 c -42819.1 d 79104.77 e
Which should be impossible...