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Finding the Fourth Proportional to 686.34, 1,029.42 and 397.80

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Solution

The fourth proportional to 686.34, 1,029.42 and 397.80 is: 596.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.34 : 1,029.42 = 397.80 : x
  2. Step 2: Convert to fraction form
    686.34/1,029.42 = 397.80/x
  3. Step 3: Cross multiply
    686.34x = 1,029.42 × 397.80
  4. Step 4: Simplify right side
    686.34x = 409,503.28
  5. Step 5: Solve for x
    x = 409,503.28/686.34
  6. Step 6: Final answer
    x = 596.65

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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.