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Finding the Third Proportional to 82,709 and 181,177

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Solution

The third proportional to 82,709 and 181,177 is: 396,874.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,709 : 181,177 = 181,177 : x
  2. Step 2: Convert to fraction form
    82,709/181,177 = 181,177/x
  3. Step 3: Cross multiply
    82,709x = 181,177 × 181,177
  4. Step 4: Simplify right side
    82,709x = 32,825,105,329
  5. Step 5: Solve for x
    x = 32,825,105,329/82,709
  6. Step 6: Final answer
    x = 396,874.65

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.