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Finding the Third Proportional to 82,017 and 128,493

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Solution

The third proportional to 82,017 and 128,493 is: 201,305.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,017 : 128,493 = 128,493 : x
  2. Step 2: Convert to fraction form
    82,017/128,493 = 128,493/x
  3. Step 3: Cross multiply
    82,017x = 128,493 × 128,493
  4. Step 4: Simplify right side
    82,017x = 16,510,451,049
  5. Step 5: Solve for x
    x = 16,510,451,049/82,017
  6. Step 6: Final answer
    x = 201,305.23

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.