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Finding the Third Proportional to 82,519 and 128,709

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Solution

The third proportional to 82,519 and 128,709 is: 200,753.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,519 : 128,709 = 128,709 : x
  2. Step 2: Convert to fraction form
    82,519/128,709 = 128,709/x
  3. Step 3: Cross multiply
    82,519x = 128,709 × 128,709
  4. Step 4: Simplify right side
    82,519x = 16,566,006,681
  5. Step 5: Solve for x
    x = 16,566,006,681/82,519
  6. Step 6: Final answer
    x = 200,753.85

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.