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Finding the Third Proportional to 4,198 and 10,180

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Solution

The third proportional to 4,198 and 10,180 is: 24,686.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,198 : 10,180 = 10,180 : x
  2. Step 2: Convert to fraction form
    4,198/10,180 = 10,180/x
  3. Step 3: Cross multiply
    4,198x = 10,180 × 10,180
  4. Step 4: Simplify right side
    4,198x = 103,632,400
  5. Step 5: Solve for x
    x = 103,632,400/4,198
  6. Step 6: Final answer
    x = 24,686.14

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.