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Finding the Fourth Proportional to 683.60, 1,024.80 and 409.40

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Solution

The fourth proportional to 683.60, 1,024.80 and 409.40 is: 613.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.60 : 1,024.80 = 409.40 : x
  2. Step 2: Convert to fraction form
    683.60/1,024.80 = 409.40/x
  3. Step 3: Cross multiply
    683.60x = 1,024.80 × 409.40
  4. Step 4: Simplify right side
    683.60x = 419,553.12
  5. Step 5: Solve for x
    x = 419,553.12/683.60
  6. Step 6: Final answer
    x = 613.74

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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.