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Finding the Third Proportional to 49,877 and 83,124

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Solution

The third proportional to 49,877 and 83,124 is: 138,532.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,877 : 83,124 = 83,124 : x
  2. Step 2: Convert to fraction form
    49,877/83,124 = 83,124/x
  3. Step 3: Cross multiply
    49,877x = 83,124 × 83,124
  4. Step 4: Simplify right side
    49,877x = 6,909,599,376
  5. Step 5: Solve for x
    x = 6,909,599,376/49,877
  6. Step 6: Final answer
    x = 138,532.78

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.