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Finding the Third Proportional to 37,832 and 82,214

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Solution

The third proportional to 37,832 and 82,214 is: 178,662.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,832 : 82,214 = 82,214 : x
  2. Step 2: Convert to fraction form
    37,832/82,214 = 82,214/x
  3. Step 3: Cross multiply
    37,832x = 82,214 × 82,214
  4. Step 4: Simplify right side
    37,832x = 6,759,141,796
  5. Step 5: Solve for x
    x = 6,759,141,796/37,832
  6. Step 6: Final answer
    x = 178,662.03

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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.