Let's solve the problem step by step.
1. Initial Stock Price:
The initial stock price is given as [tex]\(\$ 33 \frac{3}{8}\)[/tex]. To make calculations easier, we convert this mixed number into an improper fraction and then to a decimal:
[tex]\[
33 \frac{3}{8} = 33 + \frac{3}{8} = 33 + 0.375 = 33.375
\][/tex]
So, the initial stock price is [tex]\(\$ 33.375\)[/tex].
2. Stock Increase:
By the movie's lunchtime preview, the stock rose by [tex]\(\$ 4 \frac{1}{4}\)[/tex]. Converting this to a decimal:
[tex]\[
4 \frac{1}{4} = 4 + \frac{1}{4} = 4 + 0.25 = 4.25
\][/tex]
So, the increase in stock price is [tex]\(\$ 4.25\)[/tex].
3. Stock Price at Noon:
To find the stock price at noon, we add the increase to the initial stock price:
[tex]\[
33.375 + 4.25 = 37.625
\][/tex]
So, the noon stock price is [tex]\(\$ 37.625\)[/tex].
4. Stock Decrease:
After a controversial scene was leaked in the afternoon, the stock decreased by [tex]\(\$ 8 \frac{7}{8}\)[/tex]. Converting this to a decimal:
[tex]\[
8 \frac{7}{8} = 8 + \frac{7}{8} = 8 + 0.875 = 8.875
\][/tex]
So, the decrease in stock price is [tex]\(\$ 8.875\)[/tex].
5. End of Day Stock Price:
To determine the stock price at the end of the day, we subtract the decrease from the noon stock price:
[tex]\[
37.625 - 8.875 = 28.75
\][/tex]
So, the stock price at the end of the day is [tex]\(\$ 28.75\)[/tex].
Given the options:
- [tex]\(\$ 32 \frac{1}{2}\)[/tex]
- [tex]\(\$ 31 \frac{1}{2}\)[/tex]
- [tex]\(\$ 30 \frac{1}{2}\)[/tex]
- [tex]\(\$ 28 \frac{3}{4}\)[/tex]
The correct answer is:
[tex]\(\$ 28 \frac{3}{4}\)[/tex], which is the same as [tex]\(\$ 28.75\)[/tex].
