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Finding the Third Proportional to 137 and 206

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Solution

The third proportional to 137 and 206 is: 309.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    137 : 206 = 206 : x
  2. Step 2: Convert to fraction form
    137/206 = 206/x
  3. Step 3: Cross multiply
    137x = 206 × 206
  4. Step 4: Simplify right side
    137x = 42,436
  5. Step 5: Solve for x
    x = 42,436/137
  6. Step 6: Final answer
    x = 309.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.