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Finding the Third Proportional to 1,006 and 1,782

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Solution

The third proportional to 1,006 and 1,782 is: 3,156.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,006 : 1,782 = 1,782 : x
  2. Step 2: Convert to fraction form
    1,006/1,782 = 1,782/x
  3. Step 3: Cross multiply
    1,006x = 1,782 × 1,782
  4. Step 4: Simplify right side
    1,006x = 3,175,524
  5. Step 5: Solve for x
    x = 3,175,524/1,006
  6. Step 6: Final answer
    x = 3,156.58

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.