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Finding the Third Proportional to 4,194 and 5,827

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Solution

The third proportional to 4,194 and 5,827 is: 8,095.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,194 : 5,827 = 5,827 : x
  2. Step 2: Convert to fraction form
    4,194/5,827 = 5,827/x
  3. Step 3: Cross multiply
    4,194x = 5,827 × 5,827
  4. Step 4: Simplify right side
    4,194x = 33,953,929
  5. Step 5: Solve for x
    x = 33,953,929/4,194
  6. Step 6: Final answer
    x = 8,095.83

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.