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Finding the Third Proportional to 97,414 and 209,876

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Solution

The third proportional to 97,414 and 209,876 is: 452,172.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,414 : 209,876 = 209,876 : x
  2. Step 2: Convert to fraction form
    97,414/209,876 = 209,876/x
  3. Step 3: Cross multiply
    97,414x = 209,876 × 209,876
  4. Step 4: Simplify right side
    97,414x = 44,047,935,376
  5. Step 5: Solve for x
    x = 44,047,935,376/97,414
  6. Step 6: Final answer
    x = 452,172.54

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.