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Finding the Third Proportional to 822 and 1,782

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Solution

The third proportional to 822 and 1,782 is: 3,863.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    822 : 1,782 = 1,782 : x
  2. Step 2: Convert to fraction form
    822/1,782 = 1,782/x
  3. Step 3: Cross multiply
    822x = 1,782 × 1,782
  4. Step 4: Simplify right side
    822x = 3,175,524
  5. Step 5: Solve for x
    x = 3,175,524/822
  6. Step 6: Final answer
    x = 3,863.17

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.