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Finding the Third Proportional to 97,462 and 213,537

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Solution

The third proportional to 97,462 and 213,537 is: 467,854.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,462 : 213,537 = 213,537 : x
  2. Step 2: Convert to fraction form
    97,462/213,537 = 213,537/x
  3. Step 3: Cross multiply
    97,462x = 213,537 × 213,537
  4. Step 4: Simplify right side
    97,462x = 45,598,050,369
  5. Step 5: Solve for x
    x = 45,598,050,369/97,462
  6. Step 6: Final answer
    x = 467,854.65

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.