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Finding the Third Proportional to 4,214 and 5,934

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Solution

The third proportional to 4,214 and 5,934 is: 8,356.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 5,934 = 5,934 : x
  2. Step 2: Convert to fraction form
    4,214/5,934 = 5,934/x
  3. Step 3: Cross multiply
    4,214x = 5,934 × 5,934
  4. Step 4: Simplify right side
    4,214x = 35,212,356
  5. Step 5: Solve for x
    x = 35,212,356/4,214
  6. Step 6: Final answer
    x = 8,356.04

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.