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Finding the Third Proportional to 81,414 and 121,965

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Solution

The third proportional to 81,414 and 121,965 is: 182,713.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,414 : 121,965 = 121,965 : x
  2. Step 2: Convert to fraction form
    81,414/121,965 = 121,965/x
  3. Step 3: Cross multiply
    81,414x = 121,965 × 121,965
  4. Step 4: Simplify right side
    81,414x = 14,875,461,225
  5. Step 5: Solve for x
    x = 14,875,461,225/81,414
  6. Step 6: Final answer
    x = 182,713.80

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.