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Finding the Fourth Proportional to 729.29, 1,006.39 and 414.56

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Solution

The fourth proportional to 729.29, 1,006.39 and 414.56 is: 572.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.29 : 1,006.39 = 414.56 : x
  2. Step 2: Convert to fraction form
    729.29/1,006.39 = 414.56/x
  3. Step 3: Cross multiply
    729.29x = 1,006.39 × 414.56
  4. Step 4: Simplify right side
    729.29x = 417,202.97
  5. Step 5: Solve for x
    x = 417,202.97/729.29
  6. Step 6: Final answer
    x = 572.07

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.