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Finding the Third Proportional to 83,194 and 178,857

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Solution

The third proportional to 83,194 and 178,857 is: 384,520.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,194 : 178,857 = 178,857 : x
  2. Step 2: Convert to fraction form
    83,194/178,857 = 178,857/x
  3. Step 3: Cross multiply
    83,194x = 178,857 × 178,857
  4. Step 4: Simplify right side
    83,194x = 31,989,826,449
  5. Step 5: Solve for x
    x = 31,989,826,449/83,194
  6. Step 6: Final answer
    x = 384,520.84

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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.