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Otto's investment portfolio consisted of shares of internet stock and copper stock. During the year, the value of his internet shares increased $10\%$, but the value of his copper shares decreased from $\$10{,}000$ to $\$9{,}000$. During the same year, the total value of his portfolio increased by $6\%$. What was the dollar value of his internet shares at the end of the year?

 Mar 25, 2020
 #1
avatar+111330 
+1

Let I be the value of  his internet stocks at the start of the year

Let P  be the value of his portfolio at the start of the  year

 

So......at the start of  the year  the value of his portfolio  was

 

I  +  10000  =  P       (1)

 

At the end of the year, since his portfolio  decreased  by 6%  from the start  of the year....it is now worth  .94P

And his internet stock is now worth 1.10 I   since it increased  by 10%

 

So.....at the end of the year we  have  that

 

1.10 I   + 9000   =.94P      (2)        sub (1)  into (2)

 

1.10 I   +  9000   =  .94  ( I + 10000)     simplify

 

1.10 I   + 9000  = .94 I  +  9400     subtract   9000,  .94 I    from both sides

 

.16 I  =   400        divide both sides  by   16

 

I   = $2500    =   value of internet stock at the start of the year

 

So....at  the end of the year, they were worth  1.10 * 2500  = $2750

 

 

cool cool cool

 Mar 25, 2020
 #2
avatar+1970 
+1

NIce, CPhill!

CalTheGreat  Mar 25, 2020
 #3
avatar
0

Oh, that was wrong. Somehow, it was 44,000 dollars

 Mar 25, 2020

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