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Finding the Third Proportional to 13,664 and 19,214

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Solution

The third proportional to 13,664 and 19,214 is: 27,018.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,664 : 19,214 = 19,214 : x
  2. Step 2: Convert to fraction form
    13,664/19,214 = 19,214/x
  3. Step 3: Cross multiply
    13,664x = 19,214 × 19,214
  4. Step 4: Simplify right side
    13,664x = 369,177,796
  5. Step 5: Solve for x
    x = 369,177,796/13,664
  6. Step 6: Final answer
    x = 27,018.28

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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.