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Finding the Third Proportional to 197.06 and 413.13

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Solution

The third proportional to 197.06 and 413.13 is: 866.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    197.06 : 413.13 = 413.13 : x
  2. Step 2: Convert to fraction form
    197.06/413.13 = 413.13/x
  3. Step 3: Cross multiply
    197.06x = 413.13 × 413.13
  4. Step 4: Simplify right side
    197.06x = 170,672.27
  5. Step 5: Solve for x
    x = 170,672.27/197.06
  6. Step 6: Final answer
    x = 866.08

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.