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Finding the Third Proportional to 6,738 and 7,442

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Solution

The third proportional to 6,738 and 7,442 is: 8,219.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,738 : 7,442 = 7,442 : x
  2. Step 2: Convert to fraction form
    6,738/7,442 = 7,442/x
  3. Step 3: Cross multiply
    6,738x = 7,442 × 7,442
  4. Step 4: Simplify right side
    6,738x = 55,383,364
  5. Step 5: Solve for x
    x = 55,383,364/6,738
  6. Step 6: Final answer
    x = 8,219.56

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.