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Finding the Third Proportional to 83,902 and 186,452

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Solution

The third proportional to 83,902 and 186,452 is: 414,344.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,902 : 186,452 = 186,452 : x
  2. Step 2: Convert to fraction form
    83,902/186,452 = 186,452/x
  3. Step 3: Cross multiply
    83,902x = 186,452 × 186,452
  4. Step 4: Simplify right side
    83,902x = 34,764,348,304
  5. Step 5: Solve for x
    x = 34,764,348,304/83,902
  6. Step 6: Final answer
    x = 414,344.69

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.