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Finding the Third Proportional to 82,032 and 120,744

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Solution

The third proportional to 82,032 and 120,744 is: 177,724.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,032 : 120,744 = 120,744 : x
  2. Step 2: Convert to fraction form
    82,032/120,744 = 120,744/x
  3. Step 3: Cross multiply
    82,032x = 120,744 × 120,744
  4. Step 4: Simplify right side
    82,032x = 14,579,113,536
  5. Step 5: Solve for x
    x = 14,579,113,536/82,032
  6. Step 6: Final answer
    x = 177,724.71

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.