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Finding the Third Proportional to 6,400 and 13,824

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Solution

The third proportional to 6,400 and 13,824 is: 29,859.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,400 : 13,824 = 13,824 : x
  2. Step 2: Convert to fraction form
    6,400/13,824 = 13,824/x
  3. Step 3: Cross multiply
    6,400x = 13,824 × 13,824
  4. Step 4: Simplify right side
    6,400x = 191,102,976
  5. Step 5: Solve for x
    x = 191,102,976/6,400
  6. Step 6: Final answer
    x = 29,859.84

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.