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Finding the Third Proportional to 2,405 and 3,689

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Solution

The third proportional to 2,405 and 3,689 is: 5,658.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,405 : 3,689 = 3,689 : x
  2. Step 2: Convert to fraction form
    2,405/3,689 = 3,689/x
  3. Step 3: Cross multiply
    2,405x = 3,689 × 3,689
  4. Step 4: Simplify right side
    2,405x = 13,608,721
  5. Step 5: Solve for x
    x = 13,608,721/2,405
  6. Step 6: Final answer
    x = 5,658.51

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.