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Finding the Third Proportional to 83,776 and 182,304

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Solution

The third proportional to 83,776 and 182,304 is: 396,709.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,776 : 182,304 = 182,304 : x
  2. Step 2: Convert to fraction form
    83,776/182,304 = 182,304/x
  3. Step 3: Cross multiply
    83,776x = 182,304 × 182,304
  4. Step 4: Simplify right side
    83,776x = 33,234,748,416
  5. Step 5: Solve for x
    x = 33,234,748,416/83,776
  6. Step 6: Final answer
    x = 396,709.66

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.