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Finding the Third Proportional to 1,408 and 3,412

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Solution

The third proportional to 1,408 and 3,412 is: 8,268.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,408 : 3,412 = 3,412 : x
  2. Step 2: Convert to fraction form
    1,408/3,412 = 3,412/x
  3. Step 3: Cross multiply
    1,408x = 3,412 × 3,412
  4. Step 4: Simplify right side
    1,408x = 11,641,744
  5. Step 5: Solve for x
    x = 11,641,744/1,408
  6. Step 6: Final answer
    x = 8,268.28

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.