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Finding the Fourth Proportional to 686.85, 1,029.22 and 408.64

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Solution

The fourth proportional to 686.85, 1,029.22 and 408.64 is: 612.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.85 : 1,029.22 = 408.64 : x
  2. Step 2: Convert to fraction form
    686.85/1,029.22 = 408.64/x
  3. Step 3: Cross multiply
    686.85x = 1,029.22 × 408.64
  4. Step 4: Simplify right side
    686.85x = 420,580.46
  5. Step 5: Solve for x
    x = 420,580.46/686.85
  6. Step 6: Final answer
    x = 612.33

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.