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Finding the Fourth Proportional to 823.78, 1,233.78 and 413.20

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Solution

The fourth proportional to 823.78, 1,233.78 and 413.20 is: 618.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.78 : 1,233.78 = 413.20 : x
  2. Step 2: Convert to fraction form
    823.78/1,233.78 = 413.20/x
  3. Step 3: Cross multiply
    823.78x = 1,233.78 × 413.20
  4. Step 4: Simplify right side
    823.78x = 509,797.90
  5. Step 5: Solve for x
    x = 509,797.90/823.78
  6. Step 6: Final answer
    x = 618.85

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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.