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Finding the Third Proportional to 2,198 and 3,581

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Solution

The third proportional to 2,198 and 3,581 is: 5,834.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,198 : 3,581 = 3,581 : x
  2. Step 2: Convert to fraction form
    2,198/3,581 = 3,581/x
  3. Step 3: Cross multiply
    2,198x = 3,581 × 3,581
  4. Step 4: Simplify right side
    2,198x = 12,823,561
  5. Step 5: Solve for x
    x = 12,823,561/2,198
  6. Step 6: Final answer
    x = 5,834.20

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.