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Finding the Third Proportional to 13,680 and 21,098

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Solution

The third proportional to 13,680 and 21,098 is: 32,538.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,680 : 21,098 = 21,098 : x
  2. Step 2: Convert to fraction form
    13,680/21,098 = 21,098/x
  3. Step 3: Cross multiply
    13,680x = 21,098 × 21,098
  4. Step 4: Simplify right side
    13,680x = 445,125,604
  5. Step 5: Solve for x
    x = 445,125,604/13,680
  6. Step 6: Final answer
    x = 32,538.42

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.