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Finding the Third Proportional to 20,500 and 27,824

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Solution

The third proportional to 20,500 and 27,824 is: 37,764.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,500 : 27,824 = 27,824 : x
  2. Step 2: Convert to fraction form
    20,500/27,824 = 27,824/x
  3. Step 3: Cross multiply
    20,500x = 27,824 × 27,824
  4. Step 4: Simplify right side
    20,500x = 774,174,976
  5. Step 5: Solve for x
    x = 774,174,976/20,500
  6. Step 6: Final answer
    x = 37,764.63

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.