Athletics

160 students (from grammar schools and technical schools) participated in an athletics competition. The proportion of girls from grammar schools was 50%, and the proportion of girls from technical schools was 10%. Determine how many students were from grammar schools and how many from technical schools, given that there were three times more girls from grammar schools than girls from technical schools.

Final Answer:

a =  60
b =  100

Step-by-step explanation:

$$\begin{gathered} r_1=50\%=\frac{50}{100}=\frac{1}{2}=0.5 \\ {r}_2=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ 160=a+b \\ {r}_1\cdot a=3\cdot r_2\cdot b \\ 0.5\cdot a=3\cdot 0.1\cdot b \\ a+b=160 \\ 0.5a-0.3b=0 \\ Row2-0.5\cdot Row1\to Row2 \\ -0.8b=-80 \\ b=\frac{-80}{-0.8}=100 \\ a=160-b=160-100=60 \\ a=60 \\ b=100 \end{gathered}$$

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