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Finding the Third Proportional to 409 and 734

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Solution

The third proportional to 409 and 734 is: 1,317.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 734 = 734 : x
  2. Step 2: Convert to fraction form
    409/734 = 734/x
  3. Step 3: Cross multiply
    409x = 734 × 734
  4. Step 4: Simplify right side
    409x = 538,756
  5. Step 5: Solve for x
    x = 538,756/409
  6. Step 6: Final answer
    x = 1,317.25

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Why These Related Problems?

These problems maintain the same ratio (1.79) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.