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Finding the Third Proportional to 3,209 and 5,866

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Solution

The third proportional to 3,209 and 5,866 is: 10,722.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,209 : 5,866 = 5,866 : x
  2. Step 2: Convert to fraction form
    3,209/5,866 = 5,866/x
  3. Step 3: Cross multiply
    3,209x = 5,866 × 5,866
  4. Step 4: Simplify right side
    3,209x = 34,409,956
  5. Step 5: Solve for x
    x = 34,409,956/3,209
  6. Step 6: Final answer
    x = 10,722.95

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Why These Related Problems?

These problems maintain the same ratio (1.83) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.