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Finding the Fourth Proportional to 823.24, 1,234.20 and 412.16

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Solution

The fourth proportional to 823.24, 1,234.20 and 412.16 is: 617.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.24 : 1,234.20 = 412.16 : x
  2. Step 2: Convert to fraction form
    823.24/1,234.20 = 412.16/x
  3. Step 3: Cross multiply
    823.24x = 1,234.20 × 412.16
  4. Step 4: Simplify right side
    823.24x = 508,687.87
  5. Step 5: Solve for x
    x = 508,687.87/823.24
  6. Step 6: Final answer
    x = 617.91

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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.