Question

A brokerage firm charges

?$100

commission for every transaction? (purchase or? sale) made. A person bought a block of stock containing over 400 shares for

?$10,900

including the commission. After one? year, he received a stock dividend of

20

shares. He then sold all of his stock for

?$2

more per share than it had cost and made a profit of

?$1220

?(after paying the? commission). How many shares did he? buy, and what was the original price of each? share?

Answer 1

Let the number of shares bought be = x and its original price be = y;
We know that xy = 10900

We know that he got a stock dividend of 20 shares so now he has x+20 shares
selling price = y + 2
Total sold value = (x+20) (y+2)
But we know that brokerage = 100 (buying) + 100 (selling) = 200
So profit after that is 1220
(x+20) ( y+2) - xy - 200 = 1220
xy + 2x + 20y + 40 - xy = 1440
2x + 20y = 1400
x+10y = 700; but we know that xy = 10900 so y= 10900/x
x + 10* 10900/x = 700
x + 109000/x = 700
x² - 700 x + 109000 = 0
Solving this we get x= 466.18 and x= 233.81;
Since x> 400 is given, we will take x~= 466
y= 10900/466 = 23.39$
Thus, number of shares bought = 466 and purcahse price = 23.39$
We know that x> 400