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Finding the Third Proportional to 10,414 and 22,678

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Solution

The third proportional to 10,414 and 22,678 is: 49,384.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,414 : 22,678 = 22,678 : x
  2. Step 2: Convert to fraction form
    10,414/22,678 = 22,678/x
  3. Step 3: Cross multiply
    10,414x = 22,678 × 22,678
  4. Step 4: Simplify right side
    10,414x = 514,291,684
  5. Step 5: Solve for x
    x = 514,291,684/10,414
  6. Step 6: Final answer
    x = 49,384.64

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.