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Finding the Third Proportional to 6,896 and 8,102

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Solution

The third proportional to 6,896 and 8,102 is: 9,518.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,896 : 8,102 = 8,102 : x
  2. Step 2: Convert to fraction form
    6,896/8,102 = 8,102/x
  3. Step 3: Cross multiply
    6,896x = 8,102 × 8,102
  4. Step 4: Simplify right side
    6,896x = 65,642,404
  5. Step 5: Solve for x
    x = 65,642,404/6,896
  6. Step 6: Final answer
    x = 9,518.91

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.