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Finding the Fourth Proportional to 729.24, 1,006.31 and 414.42

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Solution

The fourth proportional to 729.24, 1,006.31 and 414.42 is: 571.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.24 : 1,006.31 = 414.42 : x
  2. Step 2: Convert to fraction form
    729.24/1,006.31 = 414.42/x
  3. Step 3: Cross multiply
    729.24x = 1,006.31 × 414.42
  4. Step 4: Simplify right side
    729.24x = 417,034.99
  5. Step 5: Solve for x
    x = 417,034.99/729.24
  6. Step 6: Final answer
    x = 571.88

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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.