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Finding the Third Proportional to 5,194 and 7,777

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Solution

The third proportional to 5,194 and 7,777 is: 11,644.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,194 : 7,777 = 7,777 : x
  2. Step 2: Convert to fraction form
    5,194/7,777 = 7,777/x
  3. Step 3: Cross multiply
    5,194x = 7,777 × 7,777
  4. Step 4: Simplify right side
    5,194x = 60,481,729
  5. Step 5: Solve for x
    x = 60,481,729/5,194
  6. Step 6: Final answer
    x = 11,644.54

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.