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Finding the Third Proportional to 10,814 and 19,198

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Solution

The third proportional to 10,814 and 19,198 is: 34,082.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,814 : 19,198 = 19,198 : x
  2. Step 2: Convert to fraction form
    10,814/19,198 = 19,198/x
  3. Step 3: Cross multiply
    10,814x = 19,198 × 19,198
  4. Step 4: Simplify right side
    10,814x = 368,563,204
  5. Step 5: Solve for x
    x = 368,563,204/10,814
  6. Step 6: Final answer
    x = 34,082.04

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.