Let's breakdown the problem step-by-step to determine the profit Caroline would make by selling her shares.
1. Initial Value Calculation:
Caroline bought 20 shares initially at a price of \( \$10 \frac{1}{2} \) per share.
This can be represented as \( 10 + \frac{1}{2} = 10.5 \) dollars per share.
Therefore, the initial total value of her shares is:
[tex]\[
\text{Initial Total Value} = 20 \text{ shares} \times 10.5 \text{ dollars/share} = 210 \text{ dollars}
\][/tex]
2. Final Value Calculation:
After 10 months, the value of each share increased to \( \$11 \frac{1}{4} \) per share.
This can be represented as \( 11 + \frac{1}{4} = 11.25 \) dollars per share.
Therefore, the final total value of her shares is:
[tex]\[
\text{Final Total Value} = 20 \text{ shares} \times 11.25 \text{ dollars/share} = 225 \text{ dollars}
\][/tex]
3. Profit Calculation:
The profit Caroline would make by selling all her shares is the difference between the final total value and the initial total value.
[tex]\[
\text{Profit} = \text{Final Total Value} - \text{Initial Total Value} = 225 \text{ dollars} - 210 \text{ dollars} = 15 \text{ dollars}
\][/tex]
So, the profit Caroline would make from selling all her shares is \$15. Therefore, the best answer is:
D. $15
