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Finding the Fourth Proportional to 596.41, 823.43 and 409.84

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Solution

The fourth proportional to 596.41, 823.43 and 409.84 is: 565.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    596.41 : 823.43 = 409.84 : x
  2. Step 2: Convert to fraction form
    596.41/823.43 = 409.84/x
  3. Step 3: Cross multiply
    596.41x = 823.43 × 409.84
  4. Step 4: Simplify right side
    596.41x = 337,474.55
  5. Step 5: Solve for x
    x = 337,474.55/596.41
  6. Step 6: Final answer
    x = 565.84

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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.