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Finding the Third Proportional to 6,770 and 7,382

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Solution

The third proportional to 6,770 and 7,382 is: 8,049.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,770 : 7,382 = 7,382 : x
  2. Step 2: Convert to fraction form
    6,770/7,382 = 7,382/x
  3. Step 3: Cross multiply
    6,770x = 7,382 × 7,382
  4. Step 4: Simplify right side
    6,770x = 54,493,924
  5. Step 5: Solve for x
    x = 54,493,924/6,770
  6. Step 6: Final answer
    x = 8,049.32

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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.