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Finding the Third Proportional to 10,777 and 23,194

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Solution

The third proportional to 10,777 and 23,194 is: 49,917.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,777 : 23,194 = 23,194 : x
  2. Step 2: Convert to fraction form
    10,777/23,194 = 23,194/x
  3. Step 3: Cross multiply
    10,777x = 23,194 × 23,194
  4. Step 4: Simplify right side
    10,777x = 537,961,636
  5. Step 5: Solve for x
    x = 537,961,636/10,777
  6. Step 6: Final answer
    x = 49,917.57

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.