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Finding the Fourth Proportional to 686.07, 1,029.23 and 411.80

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Solution

The fourth proportional to 686.07, 1,029.23 and 411.80 is: 617.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.07 : 1,029.23 = 411.80 : x
  2. Step 2: Convert to fraction form
    686.07/1,029.23 = 411.80/x
  3. Step 3: Cross multiply
    686.07x = 1,029.23 × 411.80
  4. Step 4: Simplify right side
    686.07x = 423,829.71
  5. Step 5: Solve for x
    x = 423,829.71/686.07
  6. Step 6: Final answer
    x = 617.76

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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.