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Finding the Fourth Proportional to 683.93, 1,024.34 and 409.46

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Solution

The fourth proportional to 683.93, 1,024.34 and 409.46 is: 613.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.93 : 1,024.34 = 409.46 : x
  2. Step 2: Convert to fraction form
    683.93/1,024.34 = 409.46/x
  3. Step 3: Cross multiply
    683.93x = 1,024.34 × 409.46
  4. Step 4: Simplify right side
    683.93x = 419,419.09
  5. Step 5: Solve for x
    x = 419,419.09/683.93
  6. Step 6: Final answer
    x = 613.25

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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.