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Finding the Fourth Proportional to 512.82, 706.05 and 414.90

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Solution

The fourth proportional to 512.82, 706.05 and 414.90 is: 571.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.82 : 706.05 = 414.90 : x
  2. Step 2: Convert to fraction form
    512.82/706.05 = 414.90/x
  3. Step 3: Cross multiply
    512.82x = 706.05 × 414.90
  4. Step 4: Simplify right side
    512.82x = 292,940.15
  5. Step 5: Solve for x
    x = 292,940.15/512.82
  6. Step 6: Final answer
    x = 571.23

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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.