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Finding the Third Proportional to 383.50 and 413.88

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Solution

The third proportional to 383.50 and 413.88 is: 446.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    383.50 : 413.88 = 413.88 : x
  2. Step 2: Convert to fraction form
    383.50/413.88 = 413.88/x
  3. Step 3: Cross multiply
    383.50x = 413.88 × 413.88
  4. Step 4: Simplify right side
    383.50x = 171,292.52
  5. Step 5: Solve for x
    x = 171,292.52/383.50
  6. Step 6: Final answer
    x = 446.66

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.