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Finding the Third Proportional to 407 and 419

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Solution

The third proportional to 407 and 419 is: 431.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 419 = 419 : x
  2. Step 2: Convert to fraction form
    407/419 = 419/x
  3. Step 3: Cross multiply
    407x = 419 × 419
  4. Step 4: Simplify right side
    407x = 175,561
  5. Step 5: Solve for x
    x = 175,561/407
  6. Step 6: Final answer
    x = 431.35

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.