Children 82437

If 3 boys were added to the eighth grade, 50% of the class would be boys. If, on the other hand, 3 girls were added, they would make up 7/12 classes. How many children are there in the class?

Final Answer:

n =  33

Step-by-step explanation:

$$\begin{gathered} a+3=0.50\cdot (a+3+b) \\ b+3=\frac{7}{12}\cdot (a+b+3) \\ a+3=0.50\cdot (a+3+b) \\ b+3=7/12\cdot (a+b+3) \\ 0.5a-0.5b=-1.5 \\ 7a-5b=15 \\ Pivot:Row1\leftrightarrow Row2 \\ 7a-5b=15 \\ 0.5a-0.5b=-1.5 \\ Row2-\frac{0.5}{7}\cdot Row1\to Row2 \\ 7a-5b=15 \\ -0.14b=-2.57 \\ b=\frac{-2.57142857}{-0.14285714}=18 \\ a=\frac{15+5b}{7}=\frac{15+5\cdot 18}{7}=15 \\ a=15 \\ b=18 \\ n=a+b=15+18=33 \end{gathered}$$

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