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Finding the Third Proportional to 13,024 and 20,198

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Solution

The third proportional to 13,024 and 20,198 is: 31,323.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,024 : 20,198 = 20,198 : x
  2. Step 2: Convert to fraction form
    13,024/20,198 = 20,198/x
  3. Step 3: Cross multiply
    13,024x = 20,198 × 20,198
  4. Step 4: Simplify right side
    13,024x = 407,959,204
  5. Step 5: Solve for x
    x = 407,959,204/13,024
  6. Step 6: Final answer
    x = 31,323.65

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.