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Finding the Fourth Proportional to 729.41, 1,006.52 and 414.65

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Solution

The fourth proportional to 729.41, 1,006.52 and 414.65 is: 572.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.41 : 1,006.52 = 414.65 : x
  2. Step 2: Convert to fraction form
    729.41/1,006.52 = 414.65/x
  3. Step 3: Cross multiply
    729.41x = 1,006.52 × 414.65
  4. Step 4: Simplify right side
    729.41x = 417,353.96
  5. Step 5: Solve for x
    x = 417,353.96/729.41
  6. Step 6: Final answer
    x = 572.18

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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.