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Finding the Third Proportional to 202.50 and 214.31

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Solution

The third proportional to 202.50 and 214.31 is: 226.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    202.50 : 214.31 = 214.31 : x
  2. Step 2: Convert to fraction form
    202.50/214.31 = 214.31/x
  3. Step 3: Cross multiply
    202.50x = 214.31 × 214.31
  4. Step 4: Simplify right side
    202.50x = 45,929.85
  5. Step 5: Solve for x
    x = 45,929.85/202.50
  6. Step 6: Final answer
    x = 226.81

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Why These Related Problems?

These problems maintain the same ratio (1.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.