In June, an investor purchased 325 shares of Oracle (an information technology company) stock at $\$ 23$ per share. In August, she purchased an additional 300 shares at $\$ 23$ per share. In November, she purchased an additional 550 shares at $\$ 33$. What is the weighted mean price per share? (Round your answer to 2 decimal places.)
Weighted mean price $\quad \square$ per share
Answer
Final Answer: The weighted mean price per share is \(\boxed{27.68}\) dollars.
Step 1 ：Let's denote the number of shares bought in June, August, and November as \(shares_{june}\), \(shares_{august}\), and \(shares_{november}\) respectively. Similarly, let's denote the price per share in June, August, and November as \(price_{june}\), \(price_{august}\), and \(price_{november}\) respectively. Given that \(shares_{june} = 325\), \(shares_{august} = 300\), \(shares_{november} = 550\), \(price_{june} = 23\), \(price_{august} = 23\), and \(price_{november} = 33\).
Step 2 ：The total amount spent on shares can be calculated by multiplying the number of shares bought each time by the price per share at that time and then summing these amounts. So, the total amount spent on shares, denoted as \(total_{amount}\), is \(total_{amount} = shares_{june} \times price_{june} + shares_{august} \times price_{august} + shares_{november} \times price_{november} = 325 \times 23 + 300 \times 23 + 550 \times 33 = 32525\).
Step 3 ：The total number of shares, denoted as \(total_{shares}\), is the sum of the number of shares bought each time. So, \(total_{shares} = shares_{june} + shares_{august} + shares_{november} = 325 + 300 + 550 = 1175\).
Step 4 ：The weighted mean price per share is calculated by dividing the total amount spent on shares by the total number of shares. So, the weighted mean price per share, denoted as \(weighted_{mean_{price}}\), is \(weighted_{mean_{price}} = \frac{total_{amount}}{total_{shares}} = \frac{32525}{1175} = 27.680851063829788\).
Step 5 ：Rounding the weighted mean price per share to 2 decimal places, we get \(weighted_{mean_{price}} = 27.68\).
Step 6 ：Final Answer: The weighted mean price per share is \(\boxed{27.68}\) dollars.
