Pupils

Two classes want to collect money. Boys are four-seventh pupils. In time, a quarter of the boys and a sixth of the girls did not pay, which meant 12 sinners. How many pupils attend these two classes?

Correct answer:

x =  56

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{4}{7}\cdot \frac{1}{4}=\frac{4\cdot 1}{7\cdot 4}=\frac{4}{28}=\frac{1}{7}\doteq 0.1429 \\ {r}_2=1-\frac{4}{7}=\frac{1\cdot 7}{7}-\frac{4}{7}=\frac{7}{7}-\frac{4}{7}=\frac{7-4}{7}=\frac{3}{7}\doteq 0.4286 \\ {r}_3=r_2\cdot \frac{1}{6}=\frac{3}{7}\cdot \frac{1}{6}=\frac{3\cdot 1}{7\cdot 6}=\frac{3}{42}=\frac{1}{14}\doteq 0.0714 \\ {r}_1\cdot x+r_3\cdot x=12 \\ \frac{1}{7}\cdot x+\frac{1}{14}\cdot x=12 \\ 1/7\cdot x+1/14\cdot x=12 \\ 3x=168 \\ x=\frac{168}{3}=56 \\ x=56 \end{gathered}$$

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