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Finding the Third Proportional to 12,214 and 19,641

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Solution

The third proportional to 12,214 and 19,641 is: 31,584.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,214 : 19,641 = 19,641 : x
  2. Step 2: Convert to fraction form
    12,214/19,641 = 19,641/x
  3. Step 3: Cross multiply
    12,214x = 19,641 × 19,641
  4. Step 4: Simplify right side
    12,214x = 385,768,881
  5. Step 5: Solve for x
    x = 385,768,881/12,214
  6. Step 6: Final answer
    x = 31,584.16

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.