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Finding the Third Proportional to 54,024 and 81,782

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Solution

The third proportional to 54,024 and 81,782 is: 123,802.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,024 : 81,782 = 81,782 : x
  2. Step 2: Convert to fraction form
    54,024/81,782 = 81,782/x
  3. Step 3: Cross multiply
    54,024x = 81,782 × 81,782
  4. Step 4: Simplify right side
    54,024x = 6,688,295,524
  5. Step 5: Solve for x
    x = 6,688,295,524/54,024
  6. Step 6: Final answer
    x = 123,802.30

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.