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Finding the Third Proportional to 257.50 and 327.25

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Solution

The third proportional to 257.50 and 327.25 is: 415.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.50 : 327.25 = 327.25 : x
  2. Step 2: Convert to fraction form
    257.50/327.25 = 327.25/x
  3. Step 3: Cross multiply
    257.50x = 327.25 × 327.25
  4. Step 4: Simplify right side
    257.50x = 107,092.56
  5. Step 5: Solve for x
    x = 107,092.56/257.50
  6. Step 6: Final answer
    x = 415.89

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.