in november 2008, apple stock dropped from $105 to $95 per share, and Microsoft dropped from $21 to $20 per share. If you invested a total of $3,570 in these stocks at the end of October and sold them for $3,250 at the end of November, how many shares of each stock did you buy?
To solve this problem, let's assign variables to the number of shares for each stock. Let's use A for Apple and M for Microsoft.
According to the given information:
1. The price of Apple stock dropped from $105 to $95 per share.
2. The price of Microsoft stock dropped from $21 to $20 per share.
3. The total investment was $3,570.
4. The final value after selling the stocks was $3,250.
Let's set up the equations based on the information given:
1. 105A + 21M = 3570 (The total investment amount)
2. 95A + 20M = 3250 (The final value after selling the stocks)
Now we need to solve these two equations.
To eliminate the variable M, we will multiply equation 2 by 105 and equation 1 by 20:
1. 2100A + 420M = 71400
3. 1900A + 400M = 39050
Next, we'll subtract equation 3 from equation 1 to eliminate the variable M:
(2100A + 420M) - (1900A + 400M) = 71400 - 39050
200A + 20M = 32350
Now we have a new equation: 200A + 20M = 32350
Since the coefficients of A and M are multiples of each other, we can divide the entire equation by 20 to simplify:
10A + M = 1617.5
Now we have a new simplified equation: 10A + M = 1617.5
To find the number of shares for each stock, we need to find the values of A and M that satisfy this equation.
There can be multiple solutions for this equation. We can try different pairs of values for A and M that add up to 1617.5 until we find a solution that satisfies both equations.
Let's start with A = 100 and M = 1517.5:
10(100) + 1517.5 = 1617.5
Now we need to check whether this solution satisfies both original equations.
The total investment equation:
105(100) + 21(1517.5) = 3570
10500 + 31837.5 = 3570
42337.5 ≠ 3570
Since this solution doesn't satisfy the total investment equation, we need to try a different combination of values for A and M. We can continue this trial and error process until we find a valid solution.
Therefore, it seems that there is no valid combination of shares for Apple and Microsoft stocks that meets the given conditions.