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Finding the Third Proportional to 13,824 and 17,496

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Solution

The third proportional to 13,824 and 17,496 is: 22,143.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,824 : 17,496 = 17,496 : x
  2. Step 2: Convert to fraction form
    13,824/17,496 = 17,496/x
  3. Step 3: Cross multiply
    13,824x = 17,496 × 17,496
  4. Step 4: Simplify right side
    13,824x = 306,110,016
  5. Step 5: Solve for x
    x = 306,110,016/13,824
  6. Step 6: Final answer
    x = 22,143.38

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.