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Finding the Third Proportional to 32,096 and 69,267

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Solution

The third proportional to 32,096 and 69,267 is: 149,486.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,096 : 69,267 = 69,267 : x
  2. Step 2: Convert to fraction form
    32,096/69,267 = 69,267/x
  3. Step 3: Cross multiply
    32,096x = 69,267 × 69,267
  4. Step 4: Simplify right side
    32,096x = 4,797,917,289
  5. Step 5: Solve for x
    x = 4,797,917,289/32,096
  6. Step 6: Final answer
    x = 149,486.46

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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.