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Finding the Third Proportional to 223 and 413.25

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Solution

The third proportional to 223 and 413.25 is: 765.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    223 : 413.25 = 413.25 : x
  2. Step 2: Convert to fraction form
    223/413.25 = 413.25/x
  3. Step 3: Cross multiply
    223x = 413.25 × 413.25
  4. Step 4: Simplify right side
    223x = 170,775.56
  5. Step 5: Solve for x
    x = 170,775.56/223
  6. Step 6: Final answer
    x = 765.81

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.