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Finding the Fourth Proportional to 506.57, 698.42 and 413.21

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Solution

The fourth proportional to 506.57, 698.42 and 413.21 is: 569.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    506.57 : 698.42 = 413.21 : x
  2. Step 2: Convert to fraction form
    506.57/698.42 = 413.21/x
  3. Step 3: Cross multiply
    506.57x = 698.42 × 413.21
  4. Step 4: Simplify right side
    506.57x = 288,596.91
  5. Step 5: Solve for x
    x = 288,596.91/506.57
  6. Step 6: Final answer
    x = 569.71

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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.