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Finding the Third Proportional to 271,976 and 408,206

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Solution

The third proportional to 271,976 and 408,206 is: 612,672.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    271,976 : 408,206 = 408,206 : x
  2. Step 2: Convert to fraction form
    271,976/408,206 = 408,206/x
  3. Step 3: Cross multiply
    271,976x = 408,206 × 408,206
  4. Step 4: Simplify right side
    271,976x = 166,632,138,436
  5. Step 5: Solve for x
    x = 166,632,138,436/271,976
  6. Step 6: Final answer
    x = 612,672.22

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.