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Finding the Third Proportional to 2,022 and 3,431

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Solution

The third proportional to 2,022 and 3,431 is: 5,821.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,022 : 3,431 = 3,431 : x
  2. Step 2: Convert to fraction form
    2,022/3,431 = 3,431/x
  3. Step 3: Cross multiply
    2,022x = 3,431 × 3,431
  4. Step 4: Simplify right side
    2,022x = 11,771,761
  5. Step 5: Solve for x
    x = 11,771,761/2,022
  6. Step 6: Final answer
    x = 5,821.84

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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.