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Finding the Third Proportional to 205,906 and 312,822

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Solution

The third proportional to 205,906 and 312,822 is: 475,253.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,906 : 312,822 = 312,822 : x
  2. Step 2: Convert to fraction form
    205,906/312,822 = 312,822/x
  3. Step 3: Cross multiply
    205,906x = 312,822 × 312,822
  4. Step 4: Simplify right side
    205,906x = 97,857,603,684
  5. Step 5: Solve for x
    x = 97,857,603,684/205,906
  6. Step 6: Final answer
    x = 475,253.77

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.