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Finding the Third Proportional to 5,646 and 8,214

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Solution

The third proportional to 5,646 and 8,214 is: 11,950.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,646 : 8,214 = 8,214 : x
  2. Step 2: Convert to fraction form
    5,646/8,214 = 8,214/x
  3. Step 3: Cross multiply
    5,646x = 8,214 × 8,214
  4. Step 4: Simplify right side
    5,646x = 67,469,796
  5. Step 5: Solve for x
    x = 67,469,796/5,646
  6. Step 6: Final answer
    x = 11,950.02

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.