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Finding the Third Proportional to 109 and 196.75

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Solution

The third proportional to 109 and 196.75 is: 355.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    109 : 196.75 = 196.75 : x
  2. Step 2: Convert to fraction form
    109/196.75 = 196.75/x
  3. Step 3: Cross multiply
    109x = 196.75 × 196.75
  4. Step 4: Simplify right side
    109x = 38,710.56
  5. Step 5: Solve for x
    x = 38,710.56/109
  6. Step 6: Final answer
    x = 355.14

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.