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Finding the Third Proportional to 6,314 and 6,866

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Solution

The third proportional to 6,314 and 6,866 is: 7,466.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,314 : 6,866 = 6,866 : x
  2. Step 2: Convert to fraction form
    6,314/6,866 = 6,866/x
  3. Step 3: Cross multiply
    6,314x = 6,866 × 6,866
  4. Step 4: Simplify right side
    6,314x = 47,141,956
  5. Step 5: Solve for x
    x = 47,141,956/6,314
  6. Step 6: Final answer
    x = 7,466.26

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.