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Finding the Third Proportional to 106 and 209.75

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Solution

The third proportional to 106 and 209.75 is: 415.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 209.75 = 209.75 : x
  2. Step 2: Convert to fraction form
    106/209.75 = 209.75/x
  3. Step 3: Cross multiply
    106x = 209.75 × 209.75
  4. Step 4: Simplify right side
    106x = 43,995.06
  5. Step 5: Solve for x
    x = 43,995.06/106
  6. Step 6: Final answer
    x = 415.05

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Why These Related Problems?

These problems maintain the same ratio (1.98) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.