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Finding the Fourth Proportional to 683.15, 1,023.69 and 409.09

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Solution

The fourth proportional to 683.15, 1,023.69 and 409.09 is: 613.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.15 : 1,023.69 = 409.09 : x
  2. Step 2: Convert to fraction form
    683.15/1,023.69 = 409.09/x
  3. Step 3: Cross multiply
    683.15x = 1,023.69 × 409.09
  4. Step 4: Simplify right side
    683.15x = 418,781.34
  5. Step 5: Solve for x
    x = 418,781.34/683.15
  6. Step 6: Final answer
    x = 613.02

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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.