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Finding the Third Proportional to 3,413 and 3,689

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Solution

The third proportional to 3,413 and 3,689 is: 3,987.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,413 : 3,689 = 3,689 : x
  2. Step 2: Convert to fraction form
    3,413/3,689 = 3,689/x
  3. Step 3: Cross multiply
    3,413x = 3,689 × 3,689
  4. Step 4: Simplify right side
    3,413x = 13,608,721
  5. Step 5: Solve for x
    x = 13,608,721/3,413
  6. Step 6: Final answer
    x = 3,987.32

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.