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Finding the Fourth Proportional to 683.54, 1,024.69 and 410.16

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Solution

The fourth proportional to 683.54, 1,024.69 and 410.16 is: 614.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.54 : 1,024.69 = 410.16 : x
  2. Step 2: Convert to fraction form
    683.54/1,024.69 = 410.16/x
  3. Step 3: Cross multiply
    683.54x = 1,024.69 × 410.16
  4. Step 4: Simplify right side
    683.54x = 420,286.85
  5. Step 5: Solve for x
    x = 420,286.85/683.54
  6. Step 6: Final answer
    x = 614.87

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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.