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Finding the Third Proportional to 8,214 and 12,744

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Solution

The third proportional to 8,214 and 12,744 is: 19,772.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,214 : 12,744 = 12,744 : x
  2. Step 2: Convert to fraction form
    8,214/12,744 = 12,744/x
  3. Step 3: Cross multiply
    8,214x = 12,744 × 12,744
  4. Step 4: Simplify right side
    8,214x = 162,409,536
  5. Step 5: Solve for x
    x = 162,409,536/8,214
  6. Step 6: Final answer
    x = 19,772.28

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.