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Finding the Fourth Proportional to 596.24, 822.56 and 409.44

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Solution

The fourth proportional to 596.24, 822.56 and 409.44 is: 564.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    596.24 : 822.56 = 409.44 : x
  2. Step 2: Convert to fraction form
    596.24/822.56 = 409.44/x
  3. Step 3: Cross multiply
    596.24x = 822.56 × 409.44
  4. Step 4: Simplify right side
    596.24x = 336,788.97
  5. Step 5: Solve for x
    x = 336,788.97/596.24
  6. Step 6: Final answer
    x = 564.85

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.