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Question 963965: Joe invests $6000 into a certain amount of shares of stock A. The price of stock B is $20 more per share. If Joe has invested in stock B he would get 10 less shares for the same amount of money. Approximately how many shares of stock A did Joe buy ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he bought 60 shares of stock A and 50 shares of stock B.
stock A was worth 100 dollars.
stock B was worth 120 dollars.
60 * 100 = 6000
50 * 120 = 6000
your solution is he bought 60 shares of stock A.
how do you solve?
one way is:
let x = number of shares of stock A.
let a = price of stock A.
let (x-10) = number of shares of stock B (he bought 10 less).
let a + 20 = price of stock B (price of B was 20 more than price of A).
you get:
x*a = 6000
(x-10) * (a+20) = 6000
in the first equation, solve for a to get a = 6000/x
in the second equation, replace a with 6000/x to get:
(x-10) * (6000/x + 20) = 6000
multiply both sides of this equation to get:
(x-10) * (6000 + 20x) = 6000x
simplify to get:
6000x + 20x^2 - 60,000 - 200x = 6000x
subtract 6000x from both sides of the equation to get:
20x^2 - 6000 - 200x = 0
divide both sides of the equation by 20 and arrange the terms in descending order of degree to get:
x^2 - 10x - 3000 = 0
factor to get:
(x-60) * (x+50) = 0
solve for x to get x = 60 or x = -50
x can't be negative, so x = 60.
that is the number of shares of stock A.
the price of stock A is 6000 / 60 = 100.
for stock A you get 60 * 100 = 6000
10 less than 60 is equal to 50, so shares of stock B is equal to 50.
20 + 100 is equal to 120, so price of stock B is equal to 120.
for stock B you get 50 * 120 = 6000
solution is confirmed to be good.
solution is Joe bought 60 shares of stock A.
in order to derive that solution, you did need to find the price of stock A as well even though you weren't asked for it.
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