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Finding the Fourth Proportional to 683.14, 1,024.65 and 409.03

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Solution

The fourth proportional to 683.14, 1,024.65 and 409.03 is: 613.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.14 : 1,024.65 = 409.03 : x
  2. Step 2: Convert to fraction form
    683.14/1,024.65 = 409.03/x
  3. Step 3: Cross multiply
    683.14x = 1,024.65 × 409.03
  4. Step 4: Simplify right side
    683.14x = 419,106.86
  5. Step 5: Solve for x
    x = 419,106.86/683.14
  6. Step 6: Final answer
    x = 613.51

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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.