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Finding the Third Proportional to 114 and 206

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Solution

The third proportional to 114 and 206 is: 372.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    114 : 206 = 206 : x
  2. Step 2: Convert to fraction form
    114/206 = 206/x
  3. Step 3: Cross multiply
    114x = 206 × 206
  4. Step 4: Simplify right side
    114x = 42,436
  5. Step 5: Solve for x
    x = 42,436/114
  6. Step 6: Final answer
    x = 372.25

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.