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Finding the Third Proportional to 83,781 and 180,686

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Solution

The third proportional to 83,781 and 180,686 is: 389,675.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,781 : 180,686 = 180,686 : x
  2. Step 2: Convert to fraction form
    83,781/180,686 = 180,686/x
  3. Step 3: Cross multiply
    83,781x = 180,686 × 180,686
  4. Step 4: Simplify right side
    83,781x = 32,647,430,596
  5. Step 5: Solve for x
    x = 32,647,430,596/83,781
  6. Step 6: Final answer
    x = 389,675.83

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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.