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Finding the Third Proportional to 51,766 and 77,569

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Solution

The third proportional to 51,766 and 77,569 is: 116,233.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,766 : 77,569 = 77,569 : x
  2. Step 2: Convert to fraction form
    51,766/77,569 = 77,569/x
  3. Step 3: Cross multiply
    51,766x = 77,569 × 77,569
  4. Step 4: Simplify right side
    51,766x = 6,016,949,761
  5. Step 5: Solve for x
    x = 6,016,949,761/51,766
  6. Step 6: Final answer
    x = 116,233.62

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.