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Finding the Third Proportional to 409 and 493

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Solution

The third proportional to 409 and 493 is: 594.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 493 = 493 : x
  2. Step 2: Convert to fraction form
    409/493 = 493/x
  3. Step 3: Cross multiply
    409x = 493 × 493
  4. Step 4: Simplify right side
    409x = 243,049
  5. Step 5: Solve for x
    x = 243,049/409
  6. Step 6: Final answer
    x = 594.25

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.