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Finding the Fourth Proportional to 821.16, 1,231.94 and 409.82

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Solution

The fourth proportional to 821.16, 1,231.94 and 409.82 is: 614.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.16 : 1,231.94 = 409.82 : x
  2. Step 2: Convert to fraction form
    821.16/1,231.94 = 409.82/x
  3. Step 3: Cross multiply
    821.16x = 1,231.94 × 409.82
  4. Step 4: Simplify right side
    821.16x = 504,868.52
  5. Step 5: Solve for x
    x = 504,868.52/821.16
  6. Step 6: Final answer
    x = 614.82

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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.