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Finding the Third Proportional to 409 and 501

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Solution

The third proportional to 409 and 501 is: 613.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 501 = 501 : x
  2. Step 2: Convert to fraction form
    409/501 = 501/x
  3. Step 3: Cross multiply
    409x = 501 × 501
  4. Step 4: Simplify right side
    409x = 251,001
  5. Step 5: Solve for x
    x = 251,001/409
  6. Step 6: Final answer
    x = 613.69

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.