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Finding the Fourth Proportional to 729.65, 1,006.91 and 414.90

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Solution

The fourth proportional to 729.65, 1,006.91 and 414.90 is: 572.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.65 : 1,006.91 = 414.90 : x
  2. Step 2: Convert to fraction form
    729.65/1,006.91 = 414.90/x
  3. Step 3: Cross multiply
    729.65x = 1,006.91 × 414.90
  4. Step 4: Simplify right side
    729.65x = 417,771.61
  5. Step 5: Solve for x
    x = 417,771.61/729.65
  6. Step 6: Final answer
    x = 572.57

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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.