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Finding the Fourth Proportional to 824.14, 1,236.23 and 461.24

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Solution

The fourth proportional to 824.14, 1,236.23 and 461.24 is: 691.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.14 : 1,236.23 = 461.24 : x
  2. Step 2: Convert to fraction form
    824.14/1,236.23 = 461.24/x
  3. Step 3: Cross multiply
    824.14x = 1,236.23 × 461.24
  4. Step 4: Simplify right side
    824.14x = 570,198.73
  5. Step 5: Solve for x
    x = 570,198.73/824.14
  6. Step 6: Final answer
    x = 691.87

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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.