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Finding the Fourth Proportional to 683.86, 1,023.27 and 410.14

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Solution

The fourth proportional to 683.86, 1,023.27 and 410.14 is: 613.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.86 : 1,023.27 = 410.14 : x
  2. Step 2: Convert to fraction form
    683.86/1,023.27 = 410.14/x
  3. Step 3: Cross multiply
    683.86x = 1,023.27 × 410.14
  4. Step 4: Simplify right side
    683.86x = 419,683.96
  5. Step 5: Solve for x
    x = 419,683.96/683.86
  6. Step 6: Final answer
    x = 613.70

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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.