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Finding the Third Proportional to 37.75 and 82.25

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Solution

The third proportional to 37.75 and 82.25 is: 179.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    37.75 : 82.25 = 82.25 : x
  2. Step 2: Convert to fraction form
    37.75/82.25 = 82.25/x
  3. Step 3: Cross multiply
    37.75x = 82.25 × 82.25
  4. Step 4: Simplify right side
    37.75x = 6,765.06
  5. Step 5: Solve for x
    x = 6,765.06/37.75
  6. Step 6: Final answer
    x = 179.21

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.