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Finding the Fourth Proportional to 823.76, 1,234.07 and 412.41

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Solution

The fourth proportional to 823.76, 1,234.07 and 412.41 is: 617.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.76 : 1,234.07 = 412.41 : x
  2. Step 2: Convert to fraction form
    823.76/1,234.07 = 412.41/x
  3. Step 3: Cross multiply
    823.76x = 1,234.07 × 412.41
  4. Step 4: Simplify right side
    823.76x = 508,942.81
  5. Step 5: Solve for x
    x = 508,942.81/823.76
  6. Step 6: Final answer
    x = 617.83

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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.