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Finding the Third Proportional to 82,057 and 193,195

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Solution

The third proportional to 82,057 and 193,195 is: 454,858.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,057 : 193,195 = 193,195 : x
  2. Step 2: Convert to fraction form
    82,057/193,195 = 193,195/x
  3. Step 3: Cross multiply
    82,057x = 193,195 × 193,195
  4. Step 4: Simplify right side
    82,057x = 37,324,308,025
  5. Step 5: Solve for x
    x = 37,324,308,025/82,057
  6. Step 6: Final answer
    x = 454,858.31

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.