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Finding the Third Proportional to 2,011 and 4,111

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Solution

The third proportional to 2,011 and 4,111 is: 8,403.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,011 : 4,111 = 4,111 : x
  2. Step 2: Convert to fraction form
    2,011/4,111 = 4,111/x
  3. Step 3: Cross multiply
    2,011x = 4,111 × 4,111
  4. Step 4: Simplify right side
    2,011x = 16,900,321
  5. Step 5: Solve for x
    x = 16,900,321/2,011
  6. Step 6: Final answer
    x = 8,403.94

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.