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Finding the Third Proportional to 106 and 209.25

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Solution

The third proportional to 106 and 209.25 is: 413.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 209.25 = 209.25 : x
  2. Step 2: Convert to fraction form
    106/209.25 = 209.25/x
  3. Step 3: Cross multiply
    106x = 209.25 × 209.25
  4. Step 4: Simplify right side
    106x = 43,785.56
  5. Step 5: Solve for x
    x = 43,785.56/106
  6. Step 6: Final answer
    x = 413.07

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.