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Finding the Fourth Proportional to 686.19, 1,029.57 and 412.81

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Solution

The fourth proportional to 686.19, 1,029.57 and 412.81 is: 619.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.19 : 1,029.57 = 412.81 : x
  2. Step 2: Convert to fraction form
    686.19/1,029.57 = 412.81/x
  3. Step 3: Cross multiply
    686.19x = 1,029.57 × 412.81
  4. Step 4: Simplify right side
    686.19x = 425,016.79
  5. Step 5: Solve for x
    x = 425,016.79/686.19
  6. Step 6: Final answer
    x = 619.39

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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.