Question

Yusuf 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 19%. During the second year the value of the stock decreased by 18%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

Let's break down the problem step by step:

1. Yusuf bought the stock for \( xx \) dollars.
2. **After the first year**, the stock decreased by 19%.

To find the value after this decrease, we calculate:
\[
\text{Value after first year} = xx - (19\% \text{ of } xx) = xx - 0.19xx = (1 - 0.19)xx = 0.81xx
\]

3. **After the second year**, the stock decreased by 18%.

To find the value after the second year's decrease:
\[
\text{Value after second year} = 0.81xx - (18\% \text{ of } 0.81xx) = 0.81xx - 0.18 \times 0.81xx
\]
This can be simplified to:
\[
\text{Value after second year} = 0.81xx(1 - 0.18) = 0.81xx \times 0.82
\]

Now calculating \( 0.81 \times 0.82 \):
\[
0.81 \times 0.82 = 0.6642
\]

4. Therefore, the expression for the value of the stock after two years is:
\[
0.6642xx
\]

So, after two years, the value of the stock in terms of \( xx \) is \( 0.6642xx \).