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Finding the Third Proportional to 37.97 and 82.13

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Solution

The third proportional to 37.97 and 82.13 is: 177.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    37.97 : 82.13 = 82.13 : x
  2. Step 2: Convert to fraction form
    37.97/82.13 = 82.13/x
  3. Step 3: Cross multiply
    37.97x = 82.13 × 82.13
  4. Step 4: Simplify right side
    37.97x = 6,744.52
  5. Step 5: Solve for x
    x = 6,744.52/37.97
  6. Step 6: Final answer
    x = 177.63

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.