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Finding the Fourth Proportional to 682.00, 1,023.03 and 409.84

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Solution

The fourth proportional to 682.00, 1,023.03 and 409.84 is: 614.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    682.00 : 1,023.03 = 409.84 : x
  2. Step 2: Convert to fraction form
    682.00/1,023.03 = 409.84/x
  3. Step 3: Cross multiply
    682.00x = 1,023.03 × 409.84
  4. Step 4: Simplify right side
    682.00x = 419,276.06
  5. Step 5: Solve for x
    x = 419,276.06/682.00
  6. Step 6: Final answer
    x = 614.78

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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.