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Finding the Third Proportional to 6,214 and 8,223

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Solution

The third proportional to 6,214 and 8,223 is: 10,881.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,214 : 8,223 = 8,223 : x
  2. Step 2: Convert to fraction form
    6,214/8,223 = 8,223/x
  3. Step 3: Cross multiply
    6,214x = 8,223 × 8,223
  4. Step 4: Simplify right side
    6,214x = 67,617,729
  5. Step 5: Solve for x
    x = 67,617,729/6,214
  6. Step 6: Final answer
    x = 10,881.51

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.