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Finding the Third Proportional to 82,102 and 129,822

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Solution

The third proportional to 82,102 and 129,822 is: 205,278.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,102 : 129,822 = 129,822 : x
  2. Step 2: Convert to fraction form
    82,102/129,822 = 129,822/x
  3. Step 3: Cross multiply
    82,102x = 129,822 × 129,822
  4. Step 4: Simplify right side
    82,102x = 16,853,751,684
  5. Step 5: Solve for x
    x = 16,853,751,684/82,102
  6. Step 6: Final answer
    x = 205,278.21

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.