Sure, let's break this down step-by-step to find out how much profit Caroline would make if she sold all her shares.
1. Determine the initial price per share:
Caroline bought the shares at [tex]$10 \frac{1}{2}$[/tex], which can be written as a decimal:
[tex]\[
10 \frac{1}{2} = 10 + \frac{1}{2} = 10.5 \, \text{dollars per share}
\][/tex]
2. Determine the number of shares purchased:
Caroline bought 20 shares.
3. Calculate the initial value of the shares:
The initial value is the price per share multiplied by the number of shares:
[tex]\[
\text{Initial Value} = 20 \times 10.5 = 210 \, \text{dollars}
\][/tex]
4. Determine the final price per share:
After 10 months, the value of the stocks was [tex]$11 \frac{1}{4}$[/tex], which can be written as a decimal:
[tex]\[
11 \frac{1}{4} = 11 + \frac{1}{4} = 11.25 \, \text{dollars per share}
\][/tex]
5. Calculate the final value of the shares:
The final value is the final price per share multiplied by the number of shares:
[tex]\[
\text{Final Value} = 20 \times 11.25 = 225 \, \text{dollars}
\][/tex]
6. Calculate the profit:
The profit is the final value of the shares minus the initial value of the shares:
[tex]\[
\text{Profit} = \text{Final Value} - \text{Initial Value} = 225 - 210 = 15 \, \text{dollars}
\][/tex]
Therefore, Caroline would make a profit of [tex]\( \$15 \)[/tex] if she sold all her shares.
The correct answer is:
B. \$ 15
