Spanish learners

Two-thirds of girls and half of boys learn Spanish in the classroom. There are twice as many boys in the class as there are girls. What part of the class is learning Spanish?

Final Answer:

s =  5/9

Step-by-step explanation:

$$\begin{gathered} m+f=1 \\ m=2f \\ m=2\cdot f \\ f+m=1 \\ 2f-m=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 1.5m=1 \\ m=\frac{1}{1.5}=0.66666667 \\ f=\frac{0+m}{2}=\frac{0+0.66666667}{2}=0.33333333 \\ f=\frac{1}{3}\doteq 0.333333 \\ m=\frac{2}{3}\doteq 0.666667 \\ {f}_1=\frac{2}{3}\cdot f=\frac{2}{3}\cdot 0.3333=\frac{2}{9}\doteq 0.2222 \\ {m}_1=\frac{1}{2}\cdot m=\frac{1}{2}\cdot 0.6667=\frac{1}{3}\doteq 0.3333 \\ s=f_1+m_1=\frac{2}{9}+\frac{1}{3}=\frac{2}{9}+\frac{3}{9}=\frac{2+3}{9}=\frac{5}{9}=0.5556 \end{gathered}$$

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