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Finding the Third Proportional to 16,384 and 24,591

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Solution

The third proportional to 16,384 and 24,591 is: 36,909.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    16,384 : 24,591 = 24,591 : x
  2. Step 2: Convert to fraction form
    16,384/24,591 = 24,591/x
  3. Step 3: Cross multiply
    16,384x = 24,591 × 24,591
  4. Step 4: Simplify right side
    16,384x = 604,717,281
  5. Step 5: Solve for x
    x = 604,717,281/16,384
  6. Step 6: Final answer
    x = 36,909.01

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.