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Finding the Third Proportional to 1,031 and 2,011

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Solution

The third proportional to 1,031 and 2,011 is: 3,922.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,031 : 2,011 = 2,011 : x
  2. Step 2: Convert to fraction form
    1,031/2,011 = 2,011/x
  3. Step 3: Cross multiply
    1,031x = 2,011 × 2,011
  4. Step 4: Simplify right side
    1,031x = 4,044,121
  5. Step 5: Solve for x
    x = 4,044,121/1,031
  6. Step 6: Final answer
    x = 3,922.52

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.