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Finding the Third Proportional to 3,846 and 4,214

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Solution

The third proportional to 3,846 and 4,214 is: 4,617.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,846 : 4,214 = 4,214 : x
  2. Step 2: Convert to fraction form
    3,846/4,214 = 4,214/x
  3. Step 3: Cross multiply
    3,846x = 4,214 × 4,214
  4. Step 4: Simplify right side
    3,846x = 17,757,796
  5. Step 5: Solve for x
    x = 17,757,796/3,846
  6. Step 6: Final answer
    x = 4,617.21

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.