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Finding the Third Proportional to 82,234 and 177,157

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Solution

The third proportional to 82,234 and 177,157 is: 381,649.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,234 : 177,157 = 177,157 : x
  2. Step 2: Convert to fraction form
    82,234/177,157 = 177,157/x
  3. Step 3: Cross multiply
    82,234x = 177,157 × 177,157
  4. Step 4: Simplify right side
    82,234x = 31,384,602,649
  5. Step 5: Solve for x
    x = 31,384,602,649/82,234
  6. Step 6: Final answer
    x = 381,649.96

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.