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Finding the Third Proportional to 37,686 and 81,306

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Solution

The third proportional to 37,686 and 81,306 is: 175,414.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,686 : 81,306 = 81,306 : x
  2. Step 2: Convert to fraction form
    37,686/81,306 = 81,306/x
  3. Step 3: Cross multiply
    37,686x = 81,306 × 81,306
  4. Step 4: Simplify right side
    37,686x = 6,610,665,636
  5. Step 5: Solve for x
    x = 6,610,665,636/37,686
  6. Step 6: Final answer
    x = 175,414.36

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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.