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Finding the Third Proportional to 1,831 and 1,981

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Solution

The third proportional to 1,831 and 1,981 is: 2,143.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,831 : 1,981 = 1,981 : x
  2. Step 2: Convert to fraction form
    1,831/1,981 = 1,981/x
  3. Step 3: Cross multiply
    1,831x = 1,981 × 1,981
  4. Step 4: Simplify right side
    1,831x = 3,924,361
  5. Step 5: Solve for x
    x = 3,924,361/1,831
  6. Step 6: Final answer
    x = 2,143.29

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.