an investor purchased 300 shares of a stock for $2,604. he is buying more shares at a rate of $12.20. he…
an investor purchased 300 shares of a stock for $2,604. he is buying more shares at a rate of $12.20. he wants the average purchase price of all the shares to be $10.15. the average purchase price is the total amount spent divided by the total number of shares. which equation can he use to find the number of shares to buy to achieve his desired average purchase price? 10.15 = (2,604 + 12.20x)/(300 + x) 12.20 = (2,604 + 10.15x)/(300 + x) 12.20 = (300 + x)/(2,604 + 10.15x) 10.15 = (300 + x)/(2,604 + 12.20x)
Answer
Explanation:
Step1: Recall the average - price formula
The average purchase price is the total amount spent divided by the total number of shares. Let $x$ be the number of additional shares to be bought. The total amount spent initially is $$2604$, and the amount spent on additional shares is $12.20x$. So the total amount spent is $2604 + 12.20x$. The initial number of shares is 300, and the total number of shares after the new purchase is $300 + x$.
Step2: Set up the equation based on the desired average
The desired average purchase price is $$10.15$. Using the average - price formula, we have $10.15=\frac{2604 + 12.20x}{300 + x}$.
Answer:
$10.15=\frac{2604 + 12.20x}{300 + x}$