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Finding the Third Proportional to 82 and 98.25

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Solution

The third proportional to 82 and 98.25 is: 117.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    82 : 98.25 = 98.25 : x
  2. Step 2: Convert to fraction form
    82/98.25 = 98.25/x
  3. Step 3: Cross multiply
    82x = 98.25 × 98.25
  4. Step 4: Simplify right side
    82x = 9,653.06
  5. Step 5: Solve for x
    x = 9,653.06/82
  6. Step 6: Final answer
    x = 117.72

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.