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Finding the Third Proportional to 106 and 209

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Solution

The third proportional to 106 and 209 is: 412.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 209 = 209 : x
  2. Step 2: Convert to fraction form
    106/209 = 209/x
  3. Step 3: Cross multiply
    106x = 209 × 209
  4. Step 4: Simplify right side
    106x = 43,681
  5. Step 5: Solve for x
    x = 43,681/106
  6. Step 6: Final answer
    x = 412.08

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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.