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Finding the Fourth Proportional to 686.42, 1,029.89 and 412.71

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Solution

The fourth proportional to 686.42, 1,029.89 and 412.71 is: 619.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.42 : 1,029.89 = 412.71 : x
  2. Step 2: Convert to fraction form
    686.42/1,029.89 = 412.71/x
  3. Step 3: Cross multiply
    686.42x = 1,029.89 × 412.71
  4. Step 4: Simplify right side
    686.42x = 425,046.93
  5. Step 5: Solve for x
    x = 425,046.93/686.42
  6. Step 6: Final answer
    x = 619.22

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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.