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Finding the Third Proportional to 2,032 and 3,206

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Solution

The third proportional to 2,032 and 3,206 is: 5,058.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,032 : 3,206 = 3,206 : x
  2. Step 2: Convert to fraction form
    2,032/3,206 = 3,206/x
  3. Step 3: Cross multiply
    2,032x = 3,206 × 3,206
  4. Step 4: Simplify right side
    2,032x = 10,278,436
  5. Step 5: Solve for x
    x = 10,278,436/2,032
  6. Step 6: Final answer
    x = 5,058.29

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.