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Finding the Third Proportional to 6,786 and 7,770

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Solution

The third proportional to 6,786 and 7,770 is: 8,896.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,786 : 7,770 = 7,770 : x
  2. Step 2: Convert to fraction form
    6,786/7,770 = 7,770/x
  3. Step 3: Cross multiply
    6,786x = 7,770 × 7,770
  4. Step 4: Simplify right side
    6,786x = 60,372,900
  5. Step 5: Solve for x
    x = 60,372,900/6,786
  6. Step 6: Final answer
    x = 8,896.68

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.