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Finding the Third Proportional to 13,786 and 21,857

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Solution

The third proportional to 13,786 and 21,857 is: 34,653.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,786 : 21,857 = 21,857 : x
  2. Step 2: Convert to fraction form
    13,786/21,857 = 21,857/x
  3. Step 3: Cross multiply
    13,786x = 21,857 × 21,857
  4. Step 4: Simplify right side
    13,786x = 477,728,449
  5. Step 5: Solve for x
    x = 477,728,449/13,786
  6. Step 6: Final answer
    x = 34,653.16

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.