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Finding the Third Proportional to 5,827 and 12,194

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Solution

The third proportional to 5,827 and 12,194 is: 25,518.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,827 : 12,194 = 12,194 : x
  2. Step 2: Convert to fraction form
    5,827/12,194 = 12,194/x
  3. Step 3: Cross multiply
    5,827x = 12,194 × 12,194
  4. Step 4: Simplify right side
    5,827x = 148,693,636
  5. Step 5: Solve for x
    x = 148,693,636/5,827
  6. Step 6: Final answer
    x = 25,518.04

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.