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Finding the Fourth Proportional to 729.12, 1,006.16 and 414.38

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Solution

The fourth proportional to 729.12, 1,006.16 and 414.38 is: 571.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.12 : 1,006.16 = 414.38 : x
  2. Step 2: Convert to fraction form
    729.12/1,006.16 = 414.38/x
  3. Step 3: Cross multiply
    729.12x = 1,006.16 × 414.38
  4. Step 4: Simplify right side
    729.12x = 416,932.58
  5. Step 5: Solve for x
    x = 416,932.58/729.12
  6. Step 6: Final answer
    x = 571.83

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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.