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Finding the Third Proportional to 8,084 and 13,782

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Solution

The third proportional to 8,084 and 13,782 is: 23,496.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,084 : 13,782 = 13,782 : x
  2. Step 2: Convert to fraction form
    8,084/13,782 = 13,782/x
  3. Step 3: Cross multiply
    8,084x = 13,782 × 13,782
  4. Step 4: Simplify right side
    8,084x = 189,943,524
  5. Step 5: Solve for x
    x = 189,943,524/8,084
  6. Step 6: Final answer
    x = 23,496.23

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Why These Related Problems?

These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.