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Finding the Third Proportional to 206,814 and 311,451

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Solution

The third proportional to 206,814 and 311,451 is: 469,028.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,814 : 311,451 = 311,451 : x
  2. Step 2: Convert to fraction form
    206,814/311,451 = 311,451/x
  3. Step 3: Cross multiply
    206,814x = 311,451 × 311,451
  4. Step 4: Simplify right side
    206,814x = 97,001,725,401
  5. Step 5: Solve for x
    x = 97,001,725,401/206,814
  6. Step 6: Final answer
    x = 469,028.82

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.