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Finding the Fourth Proportional to 683.16, 1,024.02 and 409.38

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Solution

The fourth proportional to 683.16, 1,024.02 and 409.38 is: 613.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.16 : 1,024.02 = 409.38 : x
  2. Step 2: Convert to fraction form
    683.16/1,024.02 = 409.38/x
  3. Step 3: Cross multiply
    683.16x = 1,024.02 × 409.38
  4. Step 4: Simplify right side
    683.16x = 419,213.31
  5. Step 5: Solve for x
    x = 419,213.31/683.16
  6. Step 6: Final answer
    x = 613.64

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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.