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Finding the Fourth Proportional to 821.46, 1,231.31 and 409.78

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Solution

The fourth proportional to 821.46, 1,231.31 and 409.78 is: 614.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.46 : 1,231.31 = 409.78 : x
  2. Step 2: Convert to fraction form
    821.46/1,231.31 = 409.78/x
  3. Step 3: Cross multiply
    821.46x = 1,231.31 × 409.78
  4. Step 4: Simplify right side
    821.46x = 504,564.16
  5. Step 5: Solve for x
    x = 504,564.16/821.46
  6. Step 6: Final answer
    x = 614.23

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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.