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Finding the Third Proportional to 32,976 and 77,766

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Solution

The third proportional to 32,976 and 77,766 is: 183,392.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,976 : 77,766 = 77,766 : x
  2. Step 2: Convert to fraction form
    32,976/77,766 = 77,766/x
  3. Step 3: Cross multiply
    32,976x = 77,766 × 77,766
  4. Step 4: Simplify right side
    32,976x = 6,047,550,756
  5. Step 5: Solve for x
    x = 6,047,550,756/32,976
  6. Step 6: Final answer
    x = 183,392.49

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.