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Finding the Third Proportional to 263.72 and 413.54

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Solution

The third proportional to 263.72 and 413.54 is: 648.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    263.72 : 413.54 = 413.54 : x
  2. Step 2: Convert to fraction form
    263.72/413.54 = 413.54/x
  3. Step 3: Cross multiply
    263.72x = 413.54 × 413.54
  4. Step 4: Simplify right side
    263.72x = 171,017.79
  5. Step 5: Solve for x
    x = 171,017.79/263.72
  6. Step 6: Final answer
    x = 648.47

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.