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Finding the Third Proportional to 5,696 and 8,219

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Solution

The third proportional to 5,696 and 8,219 is: 11,859.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,696 : 8,219 = 8,219 : x
  2. Step 2: Convert to fraction form
    5,696/8,219 = 8,219/x
  3. Step 3: Cross multiply
    5,696x = 8,219 × 8,219
  4. Step 4: Simplify right side
    5,696x = 67,551,961
  5. Step 5: Solve for x
    x = 67,551,961/5,696
  6. Step 6: Final answer
    x = 11,859.54

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.