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Bernardo invested $2,000 in two different types of stocks. The first type cost $32 per share, and the second cost $48 per share. Between the two types, he purchased a total of 47 shares. How many shares of the $48-per-share stock did he purchase? ◻

Bernardo invested $2,000\$2,000 in two different types of stocks. The first type cost $32\$32 per share, and the second cost $48\$48 per share. Between the two types, he purchased a total of 4747 shares. How many shares of the $48\$48-per-share stock did he purchase?\newline◻

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Q. Bernardo invested $2,000\$2,000 in two different types of stocks. The first type cost $32\$32 per share, and the second cost $48\$48 per share. Between the two types, he purchased a total of 4747 shares. How many shares of the $48\$48-per-share stock did he purchase?\newline◻
  1. Define Variables: Let xx be the number of shares of the $48\$48 stock and yy be the number of shares of the $32\$32 stock. We have two equations: x+y=47x + y = 47 (total shares) and 48x+32y=200048x + 32y = 2000 (total investment).
  2. Express yy in terms of xx: To solve for xx, we can express yy in terms of xx from the first equation: y=47−xy = 47 - x.
  3. Substitute into second equation: Substitute y=47−xy = 47 - x into the second equation: 48x+32(47−x)=200048x + 32(47 - x) = 2000.
  4. Simplify and solve for x: Now, let's simplify and solve for x: 48x+1504−32x=200048x + 1504 - 32x = 2000.
  5. Combine like terms: Combine like terms: 16x+1504=200016x + 1504 = 2000.
  6. Subtract to isolate xx: Subtract 15041504 from both sides: 16x=49616x = 496.
  7. Divide to find x: Divide both sides by 1616 to find xx: x=49616x = \frac{496}{16}.
  8. Calculate final result: Calculate xx: x=31x = 31. So, Bernardo purchased 3131 shares of the $48\$48 stock.

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