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Finding the Third Proportional to 81,414 and 129,510

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Solution

The third proportional to 81,414 and 129,510 is: 206,019.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,414 : 129,510 = 129,510 : x
  2. Step 2: Convert to fraction form
    81,414/129,510 = 129,510/x
  3. Step 3: Cross multiply
    81,414x = 129,510 × 129,510
  4. Step 4: Simplify right side
    81,414x = 16,772,840,100
  5. Step 5: Solve for x
    x = 16,772,840,100/81,414
  6. Step 6: Final answer
    x = 206,019.11

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.