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Finding the Third Proportional to 206 and 462

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Solution

The third proportional to 206 and 462 is: 1,036.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    206 : 462 = 462 : x
  2. Step 2: Convert to fraction form
    206/462 = 462/x
  3. Step 3: Cross multiply
    206x = 462 × 462
  4. Step 4: Simplify right side
    206x = 213,444
  5. Step 5: Solve for x
    x = 213,444/206
  6. Step 6: Final answer
    x = 1,036.14

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Why These Related Problems?

These problems maintain the same ratio (2.24) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.