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Finding the Third Proportional to 54,416 and 77,025

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Solution

The third proportional to 54,416 and 77,025 is: 109,027.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,416 : 77,025 = 77,025 : x
  2. Step 2: Convert to fraction form
    54,416/77,025 = 77,025/x
  3. Step 3: Cross multiply
    54,416x = 77,025 × 77,025
  4. Step 4: Simplify right side
    54,416x = 5,932,850,625
  5. Step 5: Solve for x
    x = 5,932,850,625/54,416
  6. Step 6: Final answer
    x = 109,027.69

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.