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Finding the Third Proportional to 206 and 293

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Solution

The third proportional to 206 and 293 is: 416.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    206 : 293 = 293 : x
  2. Step 2: Convert to fraction form
    206/293 = 293/x
  3. Step 3: Cross multiply
    206x = 293 × 293
  4. Step 4: Simplify right side
    206x = 85,849
  5. Step 5: Solve for x
    x = 85,849/206
  6. Step 6: Final answer
    x = 416.74

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.