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Finding the Third Proportional to 14,432 and 16,384

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Solution

The third proportional to 14,432 and 16,384 is: 18,600.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,432 : 16,384 = 16,384 : x
  2. Step 2: Convert to fraction form
    14,432/16,384 = 16,384/x
  3. Step 3: Cross multiply
    14,432x = 16,384 × 16,384
  4. Step 4: Simplify right side
    14,432x = 268,435,456
  5. Step 5: Solve for x
    x = 268,435,456/14,432
  6. Step 6: Final answer
    x = 18,600.02

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.