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Finding the Third Proportional to 82,421 and 127,519

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Solution

The third proportional to 82,421 and 127,519 is: 197,293.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,421 : 127,519 = 127,519 : x
  2. Step 2: Convert to fraction form
    82,421/127,519 = 127,519/x
  3. Step 3: Cross multiply
    82,421x = 127,519 × 127,519
  4. Step 4: Simplify right side
    82,421x = 16,261,095,361
  5. Step 5: Solve for x
    x = 16,261,095,361/82,421
  6. Step 6: Final answer
    x = 197,293.11

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.