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Finding the Third Proportional to 2,037 and 4,182

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Solution

The third proportional to 2,037 and 4,182 is: 8,585.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,037 : 4,182 = 4,182 : x
  2. Step 2: Convert to fraction form
    2,037/4,182 = 4,182/x
  3. Step 3: Cross multiply
    2,037x = 4,182 × 4,182
  4. Step 4: Simplify right side
    2,037x = 17,489,124
  5. Step 5: Solve for x
    x = 17,489,124/2,037
  6. Step 6: Final answer
    x = 8,585.73

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.