The problem involves determining how many shares of two stocks (A and B) an investor owns, given the following:

1. Total number of shares owned: 200.
2. Total value of the shares: $4000.
3. Price per share of Stock A: $9.50.
4. Price per share of Stock B: $27.00.

Let:

• $x$ = the number of shares of Stock A,
• $y$ = the number of shares of Stock B.

Step 1: Write equations based on the problem:

1. Total number of shares: $x + y = 200$.
2. Total value of shares: $9.50x + 27.00y = 4000$.

Step 2: Solve the system of equations:

From the first equation: $y = 200 - x.$

Substitute $y = 200 - x$ into the second equation: $9.50x + 27(200 - x) = 4000.$

Simplify: $9.50x + 5400 - 27x = 4000.$ $-17.50x + 5400 = 4000.$ $-17.50x = -1400.$ $x = \frac{-1400}{-17.50} = 80.$

Step 3: Solve for $y$:

Using $y = 200 - x$: $y = 200 - 80 = 120.$

Final Answer:

• The investor owns 80 shares of Stock A.
• The investor owns 120 shares of Stock B.

Would you like a detailed explanation of any step or have additional questions?

Here are 5 related questions for further practice:

1. What if the total number of shares was 300 instead of 200?
2. How would the calculations change if Stock A's price per share increased to $10.50?
3. What is the total value of Stock A owned by the investor?
4. If the investor sells 40 shares of Stock B, how does it impact the total value of the shares?
5. Can you write a system of equations for a similar problem with three stocks?

Tip: For systems of equations, substituting one variable into another is an efficient way to reduce the system to a single equation.