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Finding the Third Proportional to 409 and 821

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Solution

The third proportional to 409 and 821 is: 1,648.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 821 = 821 : x
  2. Step 2: Convert to fraction form
    409/821 = 821/x
  3. Step 3: Cross multiply
    409x = 821 × 821
  4. Step 4: Simplify right side
    409x = 674,041
  5. Step 5: Solve for x
    x = 674,041/409
  6. Step 6: Final answer
    x = 1,648.02

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.