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Finding the Third Proportional to 109 and 194.25

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Solution

The third proportional to 109 and 194.25 is: 346.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    109 : 194.25 = 194.25 : x
  2. Step 2: Convert to fraction form
    109/194.25 = 194.25/x
  3. Step 3: Cross multiply
    109x = 194.25 × 194.25
  4. Step 4: Simplify right side
    109x = 37,733.06
  5. Step 5: Solve for x
    x = 37,733.06/109
  6. Step 6: Final answer
    x = 346.17

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.