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Finding the Third Proportional to 1,408 and 3,296

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Solution

The third proportional to 1,408 and 3,296 is: 7,715.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,408 : 3,296 = 3,296 : x
  2. Step 2: Convert to fraction form
    1,408/3,296 = 3,296/x
  3. Step 3: Cross multiply
    1,408x = 3,296 × 3,296
  4. Step 4: Simplify right side
    1,408x = 10,863,616
  5. Step 5: Solve for x
    x = 10,863,616/1,408
  6. Step 6: Final answer
    x = 7,715.64

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.