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Finding the Third Proportional to 205 and 209

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Solution

The third proportional to 205 and 209 is: 213.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    205 : 209 = 209 : x
  2. Step 2: Convert to fraction form
    205/209 = 209/x
  3. Step 3: Cross multiply
    205x = 209 × 209
  4. Step 4: Simplify right side
    205x = 43,681
  5. Step 5: Solve for x
    x = 43,681/205
  6. Step 6: Final answer
    x = 213.08

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Why These Related Problems?

These problems maintain the same ratio (1.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.