an investor purchased 150 shares of a stock for $17,550. they are considering buying more shares at the…

an investor purchased 150 shares of a stock for $17,550. they are considering buying more shares at the current rate of $135.43. they want the average purchase price of all the shares to be $125. the average purchase price is the total amount spent divided by the total number of shares. how many shares should the investor buy to achieve their desired average purchase price? round to the nearest whole number if necessary.

an investor purchased 150 shares of a stock for $17,550. they are considering buying more shares at the current rate of $135.43. they want the average purchase price of all the shares to be $125. the average purchase price is the total amount spent divided by the total number of shares. how many shares should the investor buy to achieve their desired average purchase price? round to the nearest whole number if necessary.

Answer

Explanation:

Step1: Define the variables

Let $x$ be the number of additional shares to be bought.

Step2: Calculate the total amount spent and total number of shares

The total amount spent initially is $17550$. The amount to be spent on additional shares is $135.43x$. So the total amount spent is $17550 + 135.43x$. The total number of shares is $150 + x$.

Step3: Set up the average - price equation

We know that the average purchase price is $\frac{\text{total amount spent}}{\text{total number of shares}}$. So, $\frac{17550+135.43x}{150 + x}=125$.

Step4: Cross - multiply

$17550+135.43x=125(150 + x)$.

Step5: Expand the right - hand side

$17550+135.43x = 18750+125x$.

Step6: Move the $x$ terms to one side and constants to the other side

$135.43x-125x=18750 - 17550$.

Step7: Simplify both sides

$10.43x=1200$.

Step8: Solve for $x$

$x=\frac{1200}{10.43}\approx115$.

Answer:

115