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Finding the Third Proportional to 409 and 521.50

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Solution

The third proportional to 409 and 521.50 is: 664.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 521.50 = 521.50 : x
  2. Step 2: Convert to fraction form
    409/521.50 = 521.50/x
  3. Step 3: Cross multiply
    409x = 521.50 × 521.50
  4. Step 4: Simplify right side
    409x = 271,962.25
  5. Step 5: Solve for x
    x = 271,962.25/409
  6. Step 6: Final answer
    x = 664.94

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.