Let's break down each part of the problem step-by-step:

1. Number of Shares without Margin (using $10,000 and a $12 commission)

If Mary uses only her own money and does not use margin, she has $10,000 to invest. Subtracting the $12 commission, the amount she has available to buy shares is:

$10,000 - 12 = 9,988$

The cost per share is $141, so the number of shares she can buy is:

$\text{Number of shares} = \frac{9,988}{141} \approx 70.9 \, \text{shares}$

So, Mary can buy 70.9 shares with her own money.

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2. Number of Shares with Margin (using $10,000 of her own money + $10,000 borrowed, and a $20 commission)

If Mary uses both her own money and the borrowed money, she has a total of:

$10,000 + 10,000 = 20,000$

Subtracting the $20 commission, the amount she has available to buy shares is:

$20,000 - 20 = 19,980$

The cost per share is $141, so the number of shares she can buy is:

$\text{Number of shares} = \frac{19,980}{141} \approx 141.7 \, \text{shares}$

So, Mary can buy 141.7 shares using margin.

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3. Profit Calculation when Selling Shares

Mary bought 141.7 shares (from Part 2) using margin. She paid an initial commission of $20 when buying and an additional $20 commission when selling.

The selling price is $157 per share, so the total amount she receives is:

$141.7 \times 157 = 22,238.9$

After subtracting the $20 selling commission:

$22,238.9 - 20 = 22,218.9$

The amount borrowed was $10,000, which she needs to repay. So, her net amount after repaying the borrowed amount is:

$22,218.9 - 10,000 = 12,218.9$

Initial Investment:

Mary's initial investment was $10,000 of her own money.

Profit:

$12,218.9 - 10,000 = 2,218.9$

Therefore, Mary made a profit of $2,218.90.

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Let me know if you'd like more details or have further questions. Here are 5 related questions for exploration:

1. How would the profit change if the stock sold for $150 per share instead of $157?
2. What if Mary did not use any margin and invested $10,000 without borrowing?
3. What would happen if the stock price dropped to $120 instead of increasing?
4. How does the commission fee affect the number of shares Mary can buy?
5. What is the percentage return on her investment?

Tip: When calculating profits using margin, always remember to subtract the borrowed amount to determine the true gain or loss.