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Finding the Fourth Proportional to 682.86, 1,024.55 and 409.15

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Solution

The fourth proportional to 682.86, 1,024.55 and 409.15 is: 613.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    682.86 : 1,024.55 = 409.15 : x
  2. Step 2: Convert to fraction form
    682.86/1,024.55 = 409.15/x
  3. Step 3: Cross multiply
    682.86x = 1,024.55 × 409.15
  4. Step 4: Simplify right side
    682.86x = 419,190.03
  5. Step 5: Solve for x
    x = 419,190.03/682.86
  6. Step 6: Final answer
    x = 613.87

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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.