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Finding the Third Proportional to 2,002 and 3,830

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Solution

The third proportional to 2,002 and 3,830 is: 7,327.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,002 : 3,830 = 3,830 : x
  2. Step 2: Convert to fraction form
    2,002/3,830 = 3,830/x
  3. Step 3: Cross multiply
    2,002x = 3,830 × 3,830
  4. Step 4: Simplify right side
    2,002x = 14,668,900
  5. Step 5: Solve for x
    x = 14,668,900/2,002
  6. Step 6: Final answer
    x = 7,327.12

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Why These Related Problems?

These problems maintain the same ratio (1.91) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.