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Finding the Fourth Proportional to 512, 706.24 and 413.88

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Solution

The fourth proportional to 512, 706.24 and 413.88 is: 570.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    512 : 706.24 = 413.88 : x
  2. Step 2: Convert to fraction form
    512/706.24 = 413.88/x
  3. Step 3: Cross multiply
    512x = 706.24 × 413.88
  4. Step 4: Simplify right side
    512x = 292,298.61
  5. Step 5: Solve for x
    x = 292,298.61/512
  6. Step 6: Final answer
    x = 570.90

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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.