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Finding the Third Proportional to 13,824 and 29,621

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Solution

The third proportional to 13,824 and 29,621 is: 63,469.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,824 : 29,621 = 29,621 : x
  2. Step 2: Convert to fraction form
    13,824/29,621 = 29,621/x
  3. Step 3: Cross multiply
    13,824x = 29,621 × 29,621
  4. Step 4: Simplify right side
    13,824x = 877,403,641
  5. Step 5: Solve for x
    x = 877,403,641/13,824
  6. Step 6: Final answer
    x = 63,469.59

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.