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Finding the Third Proportional to 206,970 and 320,823

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Solution

The third proportional to 206,970 and 320,823 is: 497,305.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,970 : 320,823 = 320,823 : x
  2. Step 2: Convert to fraction form
    206,970/320,823 = 320,823/x
  3. Step 3: Cross multiply
    206,970x = 320,823 × 320,823
  4. Step 4: Simplify right side
    206,970x = 102,927,397,329
  5. Step 5: Solve for x
    x = 102,927,397,329/206,970
  6. Step 6: Final answer
    x = 497,305.88

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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.