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Finding the Third Proportional to 83,780 and 180,684

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Solution

The third proportional to 83,780 and 180,684 is: 389,671.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,780 : 180,684 = 180,684 : x
  2. Step 2: Convert to fraction form
    83,780/180,684 = 180,684/x
  3. Step 3: Cross multiply
    83,780x = 180,684 × 180,684
  4. Step 4: Simplify right side
    83,780x = 32,646,707,856
  5. Step 5: Solve for x
    x = 32,646,707,856/83,780
  6. Step 6: Final answer
    x = 389,671.85

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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.