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Question

shanika has invested in three different stocks. stock a is currently worth 3.50. stock B is worth 5.00 per share, while stock C is were 10.00 per share. shankia purchased half as many shares of stock B then stock A and half as many shares of stock C then stock B. If her total investments are worth $578, how many shares of each stock does she own?

Answer 1

It could just as well be socks as stocks.  There are three types of items and the problem asks us to find out how many of each.  Conveniently, they are called A, B, and C.  Let's assign:

    A = number of A items

    B = number of B items

    C = number of C items

 

The value (or weight, or importance, ...) of:

    A is 3.50   [for example $3.50/stock, so with ($3.50/stock)*(A stocks), stocks cancel, leaving $]

    B is 5,00

    C is 10.00

 

Now, some relationships between A, B, and C.

    B = A/2         [ B is half as many as A]

    C = B/2

 

And, the total amount spent [$ spent on A + $ spend on B + $ spent on C]

    578 = 3.50A + 5.00B + 10.00C

 

Let's put everything in terms of A:

     B=A/2

     C=A/4

    578 = 3.5A + 5(A/2) + 10(A/4)              

 

      2312 =  14A + 10A + 10A            [multiplying everything by 4]

      2312 = 34A

       68 = A             [nice! how these problems have whole numbers]

 

Plug the value of A (68 ) to find B:

     B = A/2

     B = 34

 

And, then find C:

     C = A/4

     C = 17

 

Checking (very important):

   Is  34 = 68/2  ?  yes.

 

   Is   17 = 34/2   ?  yes

 

  Is   578 = 3.50(68) + 5.00(34) + 10.00(17)     ?

        578 = 578   ?   yes.