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Finding the Third Proportional to 21,177 and 41,823

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Solution

The third proportional to 21,177 and 41,823 is: 82,597.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,177 : 41,823 = 41,823 : x
  2. Step 2: Convert to fraction form
    21,177/41,823 = 41,823/x
  3. Step 3: Cross multiply
    21,177x = 41,823 × 41,823
  4. Step 4: Simplify right side
    21,177x = 1,749,163,329
  5. Step 5: Solve for x
    x = 1,749,163,329/21,177
  6. Step 6: Final answer
    x = 82,597.31

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.