Question

Mohal bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it decreased by 24%. During the second year the value of the stock decreased by 18%. Write an expression in terms of x 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 account for the percentage decreases in each year.

1. **First year decrease:** The stock decreased by 24%. Therefore, the value of the stock at the end of the first year can be calculated as follows:
\[
\text{Value after first year} = x - 0.24x = 0.76x
\]

2. **Second year decrease:** The stock then decreased by 18% of its value at the end of the first year. We calculate this decrease on the new value (0.76x):
\[
\text{Value after second year} = 0.76x - 0.18(0.76x) = 0.76x(1 - 0.18) = 0.76x \cdot 0.82
\]

3. **Simplifying the expression:**
\[
\text{Value after second year} = 0.76 \cdot 0.82 \cdot x
\]
Now we calculate \(0.76 \cdot 0.82\):
\[
0.76 \cdot 0.82 = 0.6232
\]

Thus, the expression for the value of the stock after two years is:
\[
0.6232x
\]

Therefore, the final expression representing the value of the stock after the two years is:
\[
\boxed{0.6232x}
\]