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Finding the Third Proportional to 2,038 and 3,782

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Solution

The third proportional to 2,038 and 3,782 is: 7,018.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,038 : 3,782 = 3,782 : x
  2. Step 2: Convert to fraction form
    2,038/3,782 = 3,782/x
  3. Step 3: Cross multiply
    2,038x = 3,782 × 3,782
  4. Step 4: Simplify right side
    2,038x = 14,303,524
  5. Step 5: Solve for x
    x = 14,303,524/2,038
  6. Step 6: Final answer
    x = 7,018.41

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.