Question

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?

Answer 1

44000

Explanation:

Let w be the initial value of Otto's internet stock, in dollars. At the beginning of the year, the total value of his portfolio is w+10,000 dollars. At the end of the year, the total value of his portfolio is 1.1w+9,000 dollars. Since increasing by 6% is equivalent to multiplying by 1.06, we have

1.06(w+10,000)=1.1w +9,000

Distributing and collecting terms, we find w=40,000. At the end of the year, his internet stock is worth 40,000* 1.1=44,000 dollars.

*credits: AoPS