Class language

Five-twelfths of the students in the class learn English, a third learn German, a sixth learn French, and two students learn Spanish. How many students are in the class, and how many languages are they learning?

Final Answer:

x =  24
a =  10
n =  8
f =  4

Step-by-step explanation:

$$\begin{gathered} s=2 \\ \frac{5}{12}\cdot x+\frac{x}{3}+\frac{x}{6}+s=x \\ \frac{5}{12}\cdot x+\frac{x}{3}+\frac{x}{6}+2=x \\ 5/12\cdot x+x/3+x/6+2=x \\ x=24 \end{gathered}$$

$a=\frac{5}{12}\cdot x=\frac{5}{12}\cdot 24=\frac{5\cdot 24}{12}=\frac{120}{12}=10$

$n=\frac{1}{3}\cdot x=\frac{1}{3}\cdot 24=\frac{1\cdot 24}{3}=\frac{24}{3}=8$

$f=\frac{1}{6}\cdot x=\frac{1}{6}\cdot 24=\frac{1\cdot 24}{6}=\frac{24}{6}=4$

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