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Finding the Third Proportional to 38,400 and 82,122

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Solution

The third proportional to 38,400 and 82,122 is: 175,625.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,400 : 82,122 = 82,122 : x
  2. Step 2: Convert to fraction form
    38,400/82,122 = 82,122/x
  3. Step 3: Cross multiply
    38,400x = 82,122 × 82,122
  4. Step 4: Simplify right side
    38,400x = 6,744,022,884
  5. Step 5: Solve for x
    x = 6,744,022,884/38,400
  6. Step 6: Final answer
    x = 175,625.60

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.