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Finding the Third Proportional to 232.50 and 413.25

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Solution

The third proportional to 232.50 and 413.25 is: 734.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    232.50 : 413.25 = 413.25 : x
  2. Step 2: Convert to fraction form
    232.50/413.25 = 413.25/x
  3. Step 3: Cross multiply
    232.50x = 413.25 × 413.25
  4. Step 4: Simplify right side
    232.50x = 170,775.56
  5. Step 5: Solve for x
    x = 170,775.56/232.50
  6. Step 6: Final answer
    x = 734.52

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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.