Question 69536: One share of A stock is worth 3 1/2 shares of B stock. If the total value of the stock is $9000, how much was invested in each company?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! One share of A stock is worth 3 1/2 shares of B stock. If the total value of the stock is $9000, how much was invested in each company?
This is a poorly designed question because it has no firm answer.
For example, suppose a share of stock in company B is worth $200. That means that a share of company A stock is worth 3 1/2 times as much or $700. Now suppose that you own 2 shares of company A stock. That means you have $1400 invested in company A. The remaining $7600 ($9000 minus $1400) must be invested in company B and at $200 per share the number of shares you have in company B is 7600/200 = 38 shares.
Using the same value for the stocks, let's now suppose that you own 4 shares of company A stock at $700 per share for a total of $2800 invested in company A. The remaining $6200 ($9000 minus $2800) must be invested in company B and at $200 per share the number of shares you have in company B is 6200/200 = 31 shares.
And a third example. At $700 per share if you owned 8 shares of company A you would have a total of $5600 invested in company A. That means the remaining $3400 is invested in company B ... so you own 17 shares of company B.
In these three examples a share of stock in company A is worth 3 1/2 times a share of stock in company B. And also in each example the total amount invested is $9000. Those are all the limits set forth in the problem, so all three examples meet the requirements of the problem. Yet the amounts invested in each company differs for the in each example. There are many more examples you could come up with.
If there were a limit on the number of shares that could be owned for each company or if the problem said that the total amount invested in company A was 3 1/2 times the total amount invested in company B that might make the problem practical. It is not a practical problem the way it is written.
I think that what was intended in this problem was to say that the amount invested in company A (call it A) was 3 1/2 (use 3.5 in place of 3 1/2) times the amount invested in company B (call it B) and the total of the two investment amounts was $9000.
In such a case you can write:
A = 3.5B
and
A + B = $9000
Substitute 3.5B for A in the second equation
3.5B + B = $9000
4.5B = $9000
B = $9000/4.5 = $2000
And since A = 3.5B then A = 3.5*$2000 = $7000
But, again, that's not what the problem says as it is currently written.
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