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Finding the Third Proportional to 829 and 1,963

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Solution

The third proportional to 829 and 1,963 is: 4,648.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,963 = 1,963 : x
  2. Step 2: Convert to fraction form
    829/1,963 = 1,963/x
  3. Step 3: Cross multiply
    829x = 1,963 × 1,963
  4. Step 4: Simplify right side
    829x = 3,853,369
  5. Step 5: Solve for x
    x = 3,853,369/829
  6. Step 6: Final answer
    x = 4,648.21

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.