School year

At the end of the school year, 20% of the 250 children who attended school were awarded. 18% of boys and 23% of girls received awards. Find the number of boys and girls who attend school.

Correct answer:

x =  150
y =  100

Step-by-step explanation:

$$\begin{gathered} q=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ {q}_1=18\%=\frac{18}{100}=\frac{9}{50}=0.18 \\ {q}_2=23\%=\frac{23}{100}=0.23 \\ n=250 \\ x+y=n \\ {q}_1\cdot x+q_2\cdot y=q\cdot n \\ x+y=250 \\ 0.18\cdot x+0.23\cdot y=0.2\cdot 250 \\ x+y=250 \\ 0.18x+0.23y=50 \\ Row2-0.18\cdot Row1\to Row2 \\ x+y=250 \\ 0.05y=5 \\ y=\frac{5}{0.05}=100 \\ x=250-y=250-100=150 \\ x=150 \\ y=100 \end{gathered}$$

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