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Finding the Third Proportional to 1,963 and 2,023

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Solution

The third proportional to 1,963 and 2,023 is: 2,084.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,963 : 2,023 = 2,023 : x
  2. Step 2: Convert to fraction form
    1,963/2,023 = 2,023/x
  3. Step 3: Cross multiply
    1,963x = 2,023 × 2,023
  4. Step 4: Simplify right side
    1,963x = 4,092,529
  5. Step 5: Solve for x
    x = 4,092,529/1,963
  6. Step 6: Final answer
    x = 2,084.83

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.