# Use matrices to solve the problem

1. Sep 20, 2009

### josh_123

Here is the problem:

Use matrices to solve the following problems:Show your matrices that you use as well as your solutions.

Classroom Example: The three major companies are coca cola, pepsi and 7up. Coca-Cola has a 40% share of the soda market, Pepsi has 40% of the soda market and 7up has the remaining 20% of the soda market. Each year, Coke retains 80% of its market, but loses 15% to pepsi and 5% to 7 up. The Pepsi company retains 90% of its market, but loses 5% to coke and 5% to 7up. The 7 up company retains 70% of its market, but loses 20% to Coke and 10% to Pepsi. After one year, what percentage of the total soda market does each company have?

After 10 years, what is the percentage of the total soda market, does each company have?

If the total soda market is 3.5 million people, what is the amount of soda pop drinkers for each company originally?After one year?After 10 years?

I've try using the cramer's rule and set it up like this:

[.80 -.15 -.05
.90 -.05 -.05
.70 -.20 -.10] this is a 3x3

multiply by
[.40
.40
.20] and this is a 3x1 so the answer will be a 3x1

[.25
.33
.18]

then multiply it by a 100 to get all the percent. I got 25% for Coke, 33% for Pepsi and 18% for 7up. I think this is wrong because when you add up the three percent up it not end up to be a 100%. Are there any way I can get this one right?please help and thank you

2. Sep 20, 2009

### josh_123

Re: Use matrices to solve the problem ASAP please

hi is anyone have an answer?I really need help