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Finding the Third Proportional to 37,857 and 81,984

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Solution

The third proportional to 37,857 and 81,984 is: 177,546.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,857 : 81,984 = 81,984 : x
  2. Step 2: Convert to fraction form
    37,857/81,984 = 81,984/x
  3. Step 3: Cross multiply
    37,857x = 81,984 × 81,984
  4. Step 4: Simplify right side
    37,857x = 6,721,376,256
  5. Step 5: Solve for x
    x = 6,721,376,256/37,857
  6. Step 6: Final answer
    x = 177,546.46

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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.