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Finding the Third Proportional to 13,564 and 19,234

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Solution

The third proportional to 13,564 and 19,234 is: 27,274.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,564 : 19,234 = 19,234 : x
  2. Step 2: Convert to fraction form
    13,564/19,234 = 19,234/x
  3. Step 3: Cross multiply
    13,564x = 19,234 × 19,234
  4. Step 4: Simplify right side
    13,564x = 369,946,756
  5. Step 5: Solve for x
    x = 369,946,756/13,564
  6. Step 6: Final answer
    x = 27,274.16

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.