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Finding the Third Proportional to 38,500 and 82,972

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Solution

The third proportional to 38,500 and 82,972 is: 178,814.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,500 : 82,972 = 82,972 : x
  2. Step 2: Convert to fraction form
    38,500/82,972 = 82,972/x
  3. Step 3: Cross multiply
    38,500x = 82,972 × 82,972
  4. Step 4: Simplify right side
    38,500x = 6,884,352,784
  5. Step 5: Solve for x
    x = 6,884,352,784/38,500
  6. Step 6: Final answer
    x = 178,814.36

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.