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Finding the Third Proportional to 10,198 and 13,724

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Solution

The third proportional to 10,198 and 13,724 is: 18,469.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,198 : 13,724 = 13,724 : x
  2. Step 2: Convert to fraction form
    10,198/13,724 = 13,724/x
  3. Step 3: Cross multiply
    10,198x = 13,724 × 13,724
  4. Step 4: Simplify right side
    10,198x = 188,348,176
  5. Step 5: Solve for x
    x = 188,348,176/10,198
  6. Step 6: Final answer
    x = 18,469.13

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.