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Finding the Third Proportional to 82,306 and 177,102

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Solution

The third proportional to 82,306 and 177,102 is: 381,079.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,306 : 177,102 = 177,102 : x
  2. Step 2: Convert to fraction form
    82,306/177,102 = 177,102/x
  3. Step 3: Cross multiply
    82,306x = 177,102 × 177,102
  4. Step 4: Simplify right side
    82,306x = 31,365,118,404
  5. Step 5: Solve for x
    x = 31,365,118,404/82,306
  6. Step 6: Final answer
    x = 381,079.37

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.