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Finding the Third Proportional to 83,686 and 128,202

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Solution

The third proportional to 83,686 and 128,202 is: 196,397.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,686 : 128,202 = 128,202 : x
  2. Step 2: Convert to fraction form
    83,686/128,202 = 128,202/x
  3. Step 3: Cross multiply
    83,686x = 128,202 × 128,202
  4. Step 4: Simplify right side
    83,686x = 16,435,752,804
  5. Step 5: Solve for x
    x = 16,435,752,804/83,686
  6. Step 6: Final answer
    x = 196,397.88

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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.