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Finding the Third Proportional to 82,809 and 180,657

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Solution

The third proportional to 82,809 and 180,657 is: 394,123.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,809 : 180,657 = 180,657 : x
  2. Step 2: Convert to fraction form
    82,809/180,657 = 180,657/x
  3. Step 3: Cross multiply
    82,809x = 180,657 × 180,657
  4. Step 4: Simplify right side
    82,809x = 32,636,951,649
  5. Step 5: Solve for x
    x = 32,636,951,649/82,809
  6. Step 6: Final answer
    x = 394,123.24

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.