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Finding the Third Proportional to 13,824 and 29,997

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Solution

The third proportional to 13,824 and 29,997 is: 65,091.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,824 : 29,997 = 29,997 : x
  2. Step 2: Convert to fraction form
    13,824/29,997 = 29,997/x
  3. Step 3: Cross multiply
    13,824x = 29,997 × 29,997
  4. Step 4: Simplify right side
    13,824x = 899,820,009
  5. Step 5: Solve for x
    x = 899,820,009/13,824
  6. Step 6: Final answer
    x = 65,091.15

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.