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Finding the Third Proportional to 51,473 and 82,198

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Solution

The third proportional to 51,473 and 82,198 is: 131,263.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,473 : 82,198 = 82,198 : x
  2. Step 2: Convert to fraction form
    51,473/82,198 = 82,198/x
  3. Step 3: Cross multiply
    51,473x = 82,198 × 82,198
  4. Step 4: Simplify right side
    51,473x = 6,756,511,204
  5. Step 5: Solve for x
    x = 6,756,511,204/51,473
  6. Step 6: Final answer
    x = 131,263.21

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.