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Finding the Third Proportional to 82 and 194

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Solution

The third proportional to 82 and 194 is: 458.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    82 : 194 = 194 : x
  2. Step 2: Convert to fraction form
    82/194 = 194/x
  3. Step 3: Cross multiply
    82x = 194 × 194
  4. Step 4: Simplify right side
    82x = 37,636
  5. Step 5: Solve for x
    x = 37,636/82
  6. Step 6: Final answer
    x = 458.98

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.