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Finding the Third Proportional to 206 and 229.75

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Solution

The third proportional to 206 and 229.75 is: 256.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    206 : 229.75 = 229.75 : x
  2. Step 2: Convert to fraction form
    206/229.75 = 229.75/x
  3. Step 3: Cross multiply
    206x = 229.75 × 229.75
  4. Step 4: Simplify right side
    206x = 52,785.06
  5. Step 5: Solve for x
    x = 52,785.06/206
  6. Step 6: Final answer
    x = 256.24

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.