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Finding the Third Proportional to 232.88 and 413.69

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Solution

The third proportional to 232.88 and 413.69 is: 734.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    232.88 : 413.69 = 413.69 : x
  2. Step 2: Convert to fraction form
    232.88/413.69 = 413.69/x
  3. Step 3: Cross multiply
    232.88x = 413.69 × 413.69
  4. Step 4: Simplify right side
    232.88x = 171,137.35
  5. Step 5: Solve for x
    x = 171,137.35/232.88
  6. Step 6: Final answer
    x = 734.89

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.