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?

Guest Mar 25, 2020

#1**+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

CPhill Mar 25, 2020