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Finding the Third Proportional to 98,523 and 213,408

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Solution

The third proportional to 98,523 and 213,408 is: 462,257.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    98,523 : 213,408 = 213,408 : x
  2. Step 2: Convert to fraction form
    98,523/213,408 = 213,408/x
  3. Step 3: Cross multiply
    98,523x = 213,408 × 213,408
  4. Step 4: Simplify right side
    98,523x = 45,542,974,464
  5. Step 5: Solve for x
    x = 45,542,974,464/98,523
  6. Step 6: Final answer
    x = 462,257.28

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.