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Finding the Third Proportional to 205.31 and 291.09

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Solution

The third proportional to 205.31 and 291.09 is: 412.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.31 : 291.09 = 291.09 : x
  2. Step 2: Convert to fraction form
    205.31/291.09 = 291.09/x
  3. Step 3: Cross multiply
    205.31x = 291.09 × 291.09
  4. Step 4: Simplify right side
    205.31x = 84,735.57
  5. Step 5: Solve for x
    x = 84,735.57/205.31
  6. Step 6: Final answer
    x = 412.72

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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.