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Finding the Third Proportional to 4,194 and 5,863

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Solution

The third proportional to 4,194 and 5,863 is: 8,196.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,194 : 5,863 = 5,863 : x
  2. Step 2: Convert to fraction form
    4,194/5,863 = 5,863/x
  3. Step 3: Cross multiply
    4,194x = 5,863 × 5,863
  4. Step 4: Simplify right side
    4,194x = 34,374,769
  5. Step 5: Solve for x
    x = 34,374,769/4,194
  6. Step 6: Final answer
    x = 8,196.18

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.