Question

John bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it decreased by 23%. During the second year the value of the stock decreased by 11%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

To find the value of the stock after two years, we need to apply the percentage decreases successively.

1. **First Year Decrease:**
The stock price decreased by 23%. This means that after one year, the value of the stock is:
\[
\text{Value after first year} = xx \times (1 - 0.23) = xx \times 0.77
\]

2. **Second Year Decrease:**
In the second year, the stock price decreased by 11%. So, we take the value after the first year and decrease it by 11%:
\[
\text{Value after second year} = (xx \times 0.77) \times (1 - 0.11) = (xx \times 0.77) \times 0.89
\]

Now, we can simplify that expression:
\[
\text{Value after second year} = xx \times 0.77 \times 0.89
\]

Calculating the product:
\[
0.77 \times 0.89 = 0.6853
\]

Therefore, the final expression that represents the value of the stock after two years is:
\[
\text{Value after two years} = xx \times 0.6853
\]

So, in conclusion, the expression in terms of \( xx \) is:
\[
xx \times 0.6853
\]