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Finding the Third Proportional to 206 and 308.25

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Solution

The third proportional to 206 and 308.25 is: 461.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    206 : 308.25 = 308.25 : x
  2. Step 2: Convert to fraction form
    206/308.25 = 308.25/x
  3. Step 3: Cross multiply
    206x = 308.25 × 308.25
  4. Step 4: Simplify right side
    206x = 95,018.06
  5. Step 5: Solve for x
    x = 95,018.06/206
  6. Step 6: Final answer
    x = 461.25

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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.