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Finding the Third Proportional to 51,822 and 82,405

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Solution

The third proportional to 51,822 and 82,405 is: 131,036.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,822 : 82,405 = 82,405 : x
  2. Step 2: Convert to fraction form
    51,822/82,405 = 82,405/x
  3. Step 3: Cross multiply
    51,822x = 82,405 × 82,405
  4. Step 4: Simplify right side
    51,822x = 6,790,584,025
  5. Step 5: Solve for x
    x = 6,790,584,025/51,822
  6. Step 6: Final answer
    x = 131,036.70

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.