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Finding the Third Proportional to 47,677 and 102,851

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Solution

The third proportional to 47,677 and 102,851 is: 221,874.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    47,677 : 102,851 = 102,851 : x
  2. Step 2: Convert to fraction form
    47,677/102,851 = 102,851/x
  3. Step 3: Cross multiply
    47,677x = 102,851 × 102,851
  4. Step 4: Simplify right side
    47,677x = 10,578,328,201
  5. Step 5: Solve for x
    x = 10,578,328,201/47,677
  6. Step 6: Final answer
    x = 221,874.87

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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.