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Finding the Third Proportional to 82,101 and 177,299

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Solution

The third proportional to 82,101 and 177,299 is: 382,881.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,101 : 177,299 = 177,299 : x
  2. Step 2: Convert to fraction form
    82,101/177,299 = 177,299/x
  3. Step 3: Cross multiply
    82,101x = 177,299 × 177,299
  4. Step 4: Simplify right side
    82,101x = 31,434,935,401
  5. Step 5: Solve for x
    x = 31,434,935,401/82,101
  6. Step 6: Final answer
    x = 382,881.27

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.