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Finding the Third Proportional to 82,257 and 178,609

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Solution

The third proportional to 82,257 and 178,609 is: 387,823.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,257 : 178,609 = 178,609 : x
  2. Step 2: Convert to fraction form
    82,257/178,609 = 178,609/x
  3. Step 3: Cross multiply
    82,257x = 178,609 × 178,609
  4. Step 4: Simplify right side
    82,257x = 31,901,174,881
  5. Step 5: Solve for x
    x = 31,901,174,881/82,257
  6. Step 6: Final answer
    x = 387,823.22

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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.