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Finding the Third Proportional to 82,005 and 177,612

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Solution

The third proportional to 82,005 and 177,612 is: 384,684.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,005 : 177,612 = 177,612 : x
  2. Step 2: Convert to fraction form
    82,005/177,612 = 177,612/x
  3. Step 3: Cross multiply
    82,005x = 177,612 × 177,612
  4. Step 4: Simplify right side
    82,005x = 31,546,022,544
  5. Step 5: Solve for x
    x = 31,546,022,544/82,005
  6. Step 6: Final answer
    x = 384,684.14

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.