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Finding the Third Proportional to 12,197 and 17,831

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Solution

The third proportional to 12,197 and 17,831 is: 26,067.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,197 : 17,831 = 17,831 : x
  2. Step 2: Convert to fraction form
    12,197/17,831 = 17,831/x
  3. Step 3: Cross multiply
    12,197x = 17,831 × 17,831
  4. Step 4: Simplify right side
    12,197x = 317,944,561
  5. Step 5: Solve for x
    x = 317,944,561/12,197
  6. Step 6: Final answer
    x = 26,067.44

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.