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Finding the Third Proportional to 13,824 and 29,853

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Solution

The third proportional to 13,824 and 29,853 is: 64,467.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,824 : 29,853 = 29,853 : x
  2. Step 2: Convert to fraction form
    13,824/29,853 = 29,853/x
  3. Step 3: Cross multiply
    13,824x = 29,853 × 29,853
  4. Step 4: Simplify right side
    13,824x = 891,201,609
  5. Step 5: Solve for x
    x = 891,201,609/13,824
  6. Step 6: Final answer
    x = 64,467.71

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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.