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Finding the Third Proportional to 54,514 and 82,042

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Solution

The third proportional to 54,514 and 82,042 is: 123,470.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,514 : 82,042 = 82,042 : x
  2. Step 2: Convert to fraction form
    54,514/82,042 = 82,042/x
  3. Step 3: Cross multiply
    54,514x = 82,042 × 82,042
  4. Step 4: Simplify right side
    54,514x = 6,730,889,764
  5. Step 5: Solve for x
    x = 6,730,889,764/54,514
  6. Step 6: Final answer
    x = 123,470.85

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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.