How Many Different Combinations of Shares Could She Buy?

Date: 03/05/98 at 16:28:35
From: Michelle Schurg
Subject: word problems using scientific notation

Mrs. Ridero has $240 that she wants to invest in three companies 
traded on the stock market. She wants to buy at least 6 shares of 
Dynamo, which sell for $24 per share, and at least 3 shares of 
Plurotron, which cost $12 per share. She also wants to buy no more 
than 10 shares of Acme, at $6 per share. Not counting commissions that 
she'd have to pay, how many different combinations of shares in the 
three companies could she buy?

Date: 03/05/98 at 22:27:26
From: Doctor Melissa
Subject: Re: word problems using scientific notation

Hi Michelle!

I know these things can seem overwhelming, so take a deep breath or 
three, and shake out your arms, and _then_ let's take a look at this.

[I must note that scientific notation has, as far as I can tell, no 
relevance to this problem -- you're not working with big enough or 
small enough numbers to need it! Perhaps you're thinking of some other 
mathematical term?]

First thing to do is evaluate where you are already. Mrs. Ridero has 
$240, that's fact one. Whatever we come up with for investment 
possibilities can't result in her investing more than $240.

Then, there are two stocks that she wants to buy a certain amount of, 
so let's look at the minimum amount for those. Dynamo costs $24 per 
share, and she wants to buy at least 6 shares, which means she's 
spending at least $144 on Dynamo. Plurotron costs $12 per share, and 
she wants to buy at least 3 shares, so that's a minimum of $36. The 
other stock, Acme, she doesn't have a minimum quantity she wants to 
buy -- she might even buy zero shares of it! What have we got to work 
with already, if she buys the minimum of the first two stocks?

       $144 + $36 = $180. 

We started out with $240, so we only have $60 of "free rein," as it 
were. Take a moment to pause and reflect: $60 is a lot less to worry 
about than $240!

If Mrs. Ridero bought those (maximum) ten shares of Acme stock, that 
would use up her $60. (She couldn't buy 9 shares of Acme and still 
invest in anything else, so I'm assuming that's not an allowable case 
-- I'm assuming she has to invest all her money.) She could buy 8 
shares of Acme for a total of $48, and have $12 left over (of the $60 
total) to buy one more shares of Plurotron at $12 per share. Here's 
where your list comes in handy:

Stock:      $6/Acme  $12/Plurotron    $24/Dynamo   Total cost
# shares    10 ($60)      0                0         $60
             8 ($48)      1 ($12)          0         $60   
             6 ($36)      2 ($24)          0         $60
             6 ($36)      0                1 ($24)   $60
             4    .....        

I bet you can finish from there! Just remember to check that each 
scenario adds up to $60, and don't skip any possibilites! If the 
multiplication gets tedious, you might notice that all the numbers 
you're working with are multiples of six, so you could relabel your 
columns 1, 2, and 4, aiming for a total of 10. If that doesn't make 
sense, ignore it.

Good luck, and write back if you need more help!

-Doctor Melissa, The Math Forum
 http://mathforum.org/dr.math/