Question 1165472: Three companies, Alpha, Beta, Gamma, are the only suppliers to a specialized market. Last Alpha's sales were $700,000, Beta's $1,200,000 and Gamma's $1,600,000.
A. What was the market share (percent of market) of each company? Note: retain all decimal places calculated in (a) to solve (b) and (c).
B. If next year's total market is expected to be $5,000,000 and each company's share remains the same, what would be the sales of each company?
C. Alpha has an aim of making its sales 75% of Beta's. With total sales as in (b) and Gamma's as in (b) what would have to be the sales of Alpha and Beta if Alpha were to make its aim?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! last year:
alpha sales = 700,000 = .7 million
beta sales = 1,200,000 = 1.2 million
gamma sales = 1,600,000 = 1.6 million
total sales = 3,500,000 = 3.5 million
all figures will be in millions.
alpha sales percent of total = .7/3.5 * 100 = 20%
beta sales = 1.2/3.5 * 100 = 34.285711429%
gamma sales = 1.6/3.5 * 100 = 45.71428571%
total percent = 100%, as it should be.
the projected sales for next year are 5 million.
if the percentages are to remain the same, then:
alpha sales are expected to be 20%/100 * 5 = 1 million.
beta sales are expected to be 35.28571142%/100 * 5 = 1.714285714 million.
gamma sales are expected to be 45.71428571%/100 * 5 = 2.285714286 million.
total sales add up to be equal to 5 million, as they should.
alpha has an aim of making its sales equal to 75% of beta sales.
total sales are expected to be 5 million.
gamma sales are expected to remain at 2.285714286 million.
the remainder of the total expected sales will be 5 million minus gamma sales = 2.714285714 million.
let x = beta sales.
then alpha aim is to get .75 * x.
together they add up to 5 million minus gama sales.
equation is:
x + .75 * x = 2.714285714 million.
combine like terms to get:
1.75 * x = that.
solve for x to get:
x = 2.714285714 / 1.75 = 1.551020408 million.
that would be beta sales.
alpha sales would be .75 * that = 1.163265306 million.
total sales would be 1.163265306 million + 1.551020408 million + 2.285714286 million = 5 million, as it should be.
alpha sales percent of beta sales = 1.163265306 million / 1.551020408 million * 100 = 75%, as it should be.
i used internal memory of the TI-84 Plus to store these intermediate results.
it makes the arithmetic much easier.
the TI-84 Plus has as many memory location as the alphabet has letters, so you can store to your heart's delight, once you know how to do it, which is not terribly hard.
there is also an online scienific calculator that could be helpful as well.
that one can be found at http://www.alcula.com/calculators/scientific-calculator/#gsc.tab=0, but you do need to have the adobe flash player activated to use it, and you do need to read the instructions on how to use it.
at any rate, your answers are above as i calculated them.
if anything, the method used should be helpful for you to determine how to solve similar problems in the future.
note that your answer are in millions.
to convert them to actual numbers, just multiply each answer by 1 million and you will be the answer in dollars.
for example:
alpha sales = 1.163265306 million.
multiply that by 1 million and you get:
alpha sales = 1,263,265.306 dollars.
round to the nearest penny and it becomes 1,263,265.31 dollars.
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