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Finding the Third Proportional to 7,682 and 16,824

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Solution

The third proportional to 7,682 and 16,824 is: 36,845.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,682 : 16,824 = 16,824 : x
  2. Step 2: Convert to fraction form
    7,682/16,824 = 16,824/x
  3. Step 3: Cross multiply
    7,682x = 16,824 × 16,824
  4. Step 4: Simplify right side
    7,682x = 283,046,976
  5. Step 5: Solve for x
    x = 283,046,976/7,682
  6. Step 6: Final answer
    x = 36,845.48

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.