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?

Question

Mathematics

Terrence Rosario

2 August, 23:11

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?

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Kendall Harper · Answer 1

44000

Step-by-step 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