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Finding the Third Proportional to 82,102 and 177,023

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Solution

The third proportional to 82,102 and 177,023 is: 381,685.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,102 : 177,023 = 177,023 : x
  2. Step 2: Convert to fraction form
    82,102/177,023 = 177,023/x
  3. Step 3: Cross multiply
    82,102x = 177,023 × 177,023
  4. Step 4: Simplify right side
    82,102x = 31,337,142,529
  5. Step 5: Solve for x
    x = 31,337,142,529/82,102
  6. Step 6: Final answer
    x = 381,685.50

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.