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Finding the Third Proportional to 11,197 and 23,311

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Solution

The third proportional to 11,197 and 23,311 is: 48,531.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    11,197 : 23,311 = 23,311 : x
  2. Step 2: Convert to fraction form
    11,197/23,311 = 23,311/x
  3. Step 3: Cross multiply
    11,197x = 23,311 × 23,311
  4. Step 4: Simplify right side
    11,197x = 543,402,721
  5. Step 5: Solve for x
    x = 543,402,721/11,197
  6. Step 6: Final answer
    x = 48,531.10

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.