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Finding the Fourth Proportional to 729, 1,006.04 and 414.21

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Solution

The fourth proportional to 729, 1,006.04 and 414.21 is: 571.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,006.04 = 414.21 : x
  2. Step 2: Convert to fraction form
    729/1,006.04 = 414.21/x
  3. Step 3: Cross multiply
    729x = 1,006.04 × 414.21
  4. Step 4: Simplify right side
    729x = 416,714.31
  5. Step 5: Solve for x
    x = 416,714.31/729
  6. Step 6: Final answer
    x = 571.62

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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.