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Finding the Fourth Proportional to 512.85, 708.54 and 413.97

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Solution

The fourth proportional to 512.85, 708.54 and 413.97 is: 571.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.85 : 708.54 = 413.97 : x
  2. Step 2: Convert to fraction form
    512.85/708.54 = 413.97/x
  3. Step 3: Cross multiply
    512.85x = 708.54 × 413.97
  4. Step 4: Simplify right side
    512.85x = 293,314.30
  5. Step 5: Solve for x
    x = 293,314.30/512.85
  6. Step 6: Final answer
    x = 571.93

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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.