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 \( 0.6642xx \).