You invested a total of 11,200 in shares of the three...

You invested a total of $\$ 11,200$ in shares of the three stocks at the given prices and expected to earn $\$ 304$ in annual dividends. If you purchased a total of 250 shares, how many shares of each stock did you purchase?

Key Concepts

Systems of Linear Equations

This concept involves setting up and solving multiple equations that represent different conditions of a problem. In financial investment problems, various constraints like total cost, dividend income, and the number of shares form a system of linear equations that can be solved simultaneously to find the unknown quantities.

Algebraic Modeling of Financial Problems

Financial problems often require translating real-world constraints into algebraic expressions. This includes representing investment totals, share counts, and expected returns with equations. Modeling these situations algebraically allows for the efficient use of mathematical methods to determine how resources are distributed or allocated.

Dividend Income Calculation

Dividend income calculation deals with determining the amount earned from dividends based on the per-share dividend rates of different stocks. In problems that combine dividend income with investment amounts and share counts, understanding how individual dividend yields contribute to total income is key to setting up the related equations.

Transcript

00:01 In this question, a case study about lesser known stocks is given.

00:05 It is given that in this given table, the price and dividend yield for different, three different stocks is given as for kt cooperation.

00:18 The price is $16 and dividend yield is 7 % per annum.

00:22 And for iff, that is international flavors and fragrances, the price is $56 and dividend yield.

00:30 Is 2 % per annum flavors and for quality systems it is $80 the price is $80 dollars and dividend yield is 2 % per annum now it is given that we invested in total the sum of $11 ,200 in shares of these three stocks and which gives the annual dividends of $304 at these given prices, if we purchased in total of 250 shares and how many shares of each stock did we purchase? so first of all, we will consider that we purchased x number of shares of kt corporations.

01:23 So let us assume that we purchased x number of shares of kt, y shares of kt, y shares of iff, z number of shares of quality systems.

02:16 So now it is given that the total sum invested is the total number of shares is 250.

02:29 So x plus y plus z should be equal to 250.

02:34 So x plus y plus z should be 250, 250.

02:45 250, 250.

02:47 So this is the first equation of this situation and it is given that the total amount invested is $11 ,200.

03:00 So the amount invested is for these three shares as the prices of shares of kt corporation is $16...

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