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Finding the Third Proportional to 83,684 and 128,198

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Solution

The third proportional to 83,684 and 128,198 is: 196,390.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,684 : 128,198 = 128,198 : x
  2. Step 2: Convert to fraction form
    83,684/128,198 = 128,198/x
  3. Step 3: Cross multiply
    83,684x = 128,198 × 128,198
  4. Step 4: Simplify right side
    83,684x = 16,434,727,204
  5. Step 5: Solve for x
    x = 16,434,727,204/83,684
  6. Step 6: Final answer
    x = 196,390.32

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.