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Finding the Third Proportional to 2,198 and 5,969

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Solution

The third proportional to 2,198 and 5,969 is: 16,209.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,198 : 5,969 = 5,969 : x
  2. Step 2: Convert to fraction form
    2,198/5,969 = 5,969/x
  3. Step 3: Cross multiply
    2,198x = 5,969 × 5,969
  4. Step 4: Simplify right side
    2,198x = 35,628,961
  5. Step 5: Solve for x
    x = 35,628,961/2,198
  6. Step 6: Final answer
    x = 16,209.72

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Why These Related Problems?

These problems maintain the same ratio (2.72) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.