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Finding the Third Proportional to 106.50 and 209.75

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Solution

The third proportional to 106.50 and 209.75 is: 413.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.50 : 209.75 = 209.75 : x
  2. Step 2: Convert to fraction form
    106.50/209.75 = 209.75/x
  3. Step 3: Cross multiply
    106.50x = 209.75 × 209.75
  4. Step 4: Simplify right side
    106.50x = 43,995.06
  5. Step 5: Solve for x
    x = 43,995.06/106.50
  6. Step 6: Final answer
    x = 413.10

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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.