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Finding the Fourth Proportional to 682.49, 1,025.10 and 409.13

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Solution

The fourth proportional to 682.49, 1,025.10 and 409.13 is: 614.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    682.49 : 1,025.10 = 409.13 : x
  2. Step 2: Convert to fraction form
    682.49/1,025.10 = 409.13/x
  3. Step 3: Cross multiply
    682.49x = 1,025.10 × 409.13
  4. Step 4: Simplify right side
    682.49x = 419,399.16
  5. Step 5: Solve for x
    x = 419,399.16/682.49
  6. Step 6: Final answer
    x = 614.51

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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.