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Finding the Third Proportional to 221.50 and 413.75

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Solution

The third proportional to 221.50 and 413.75 is: 772.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    221.50 : 413.75 = 413.75 : x
  2. Step 2: Convert to fraction form
    221.50/413.75 = 413.75/x
  3. Step 3: Cross multiply
    221.50x = 413.75 × 413.75
  4. Step 4: Simplify right side
    221.50x = 171,189.06
  5. Step 5: Solve for x
    x = 171,189.06/221.50
  6. Step 6: Final answer
    x = 772.86

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.