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Finding the Third Proportional to 270.84 and 413.86

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Solution

The third proportional to 270.84 and 413.86 is: 632.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    270.84 : 413.86 = 413.86 : x
  2. Step 2: Convert to fraction form
    270.84/413.86 = 413.86/x
  3. Step 3: Cross multiply
    270.84x = 413.86 × 413.86
  4. Step 4: Simplify right side
    270.84x = 171,279.58
  5. Step 5: Solve for x
    x = 171,279.58/270.84
  6. Step 6: Final answer
    x = 632.39

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.