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Finding the Third Proportional to 8,564 and 19,814

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Solution

The third proportional to 8,564 and 19,814 is: 45,842.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,564 : 19,814 = 19,814 : x
  2. Step 2: Convert to fraction form
    8,564/19,814 = 19,814/x
  3. Step 3: Cross multiply
    8,564x = 19,814 × 19,814
  4. Step 4: Simplify right side
    8,564x = 392,594,596
  5. Step 5: Solve for x
    x = 392,594,596/8,564
  6. Step 6: Final answer
    x = 45,842.43

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.