Question

You invested a total of 12,550 in shares of the three stocks at the given prices, and expected to earn418 in annual dividends. If you purchased a total of 300 shares, how many shares of each stock did you purchase?

Answer 1

To solve how many shares of each stock were purchased, we can set up and solve a system of equations using the given information.

Step-by-step explanation:

To solve this problem, let's use a system of equations. Let x, y, and z represent the number of shares purchased for each stock respectively.

From the problem, we know that:

x + y + z = 300 (Equation 1)

If we multiply the number of shares of each stock by their prices, the total investment will be:

(24.5x) + (13.5y) + (35.5z) = 12550 (Equation 2)

Finally, we also know that the total expected dividends are equal to $418:

0.04(24.5x) + 0.04(13.5y) + 0.04(35.5z) = 418 (Equation 3)

Solving this system of equations will give us the values for x, y, and z, which represent the number of shares purchased for each stock.