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Finding the Third Proportional to 82,217 and 177,548

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Solution

The third proportional to 82,217 and 177,548 is: 383,415.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,217 : 177,548 = 177,548 : x
  2. Step 2: Convert to fraction form
    82,217/177,548 = 177,548/x
  3. Step 3: Cross multiply
    82,217x = 177,548 × 177,548
  4. Step 4: Simplify right side
    82,217x = 31,523,292,304
  5. Step 5: Solve for x
    x = 31,523,292,304/82,217
  6. Step 6: Final answer
    x = 383,415.74

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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.