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Finding the Fourth Proportional to 824.18, 1,237.00 and 413.54

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Solution

The fourth proportional to 824.18, 1,237.00 and 413.54 is: 620.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.18 : 1,237.00 = 413.54 : x
  2. Step 2: Convert to fraction form
    824.18/1,237.00 = 413.54/x
  3. Step 3: Cross multiply
    824.18x = 1,237.00 × 413.54
  4. Step 4: Simplify right side
    824.18x = 511,546.91
  5. Step 5: Solve for x
    x = 511,546.91/824.18
  6. Step 6: Final answer
    x = 620.68

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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.