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Finding the Third Proportional to 5,682 and 8,324

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Solution

The third proportional to 5,682 and 8,324 is: 12,194.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,682 : 8,324 = 8,324 : x
  2. Step 2: Convert to fraction form
    5,682/8,324 = 8,324/x
  3. Step 3: Cross multiply
    5,682x = 8,324 × 8,324
  4. Step 4: Simplify right side
    5,682x = 69,288,976
  5. Step 5: Solve for x
    x = 69,288,976/5,682
  6. Step 6: Final answer
    x = 12,194.47

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.