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Finding the Third Proportional to 10,384 and 22,432

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Solution

The third proportional to 10,384 and 22,432 is: 48,458.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,384 : 22,432 = 22,432 : x
  2. Step 2: Convert to fraction form
    10,384/22,432 = 22,432/x
  3. Step 3: Cross multiply
    10,384x = 22,432 × 22,432
  4. Step 4: Simplify right side
    10,384x = 503,194,624
  5. Step 5: Solve for x
    x = 503,194,624/10,384
  6. Step 6: Final answer
    x = 48,458.65

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.