Four-ninths of pupils

Pupils at school choose a circle. A third of them chose athletics, four-ninths of the pupils chose ceramics, and the remaining 12 pupils chose floorball. How many pupils are there in the school? How many signed up for individual circles?

Correct answer:

n =  54
n₁ =  18
n₂ =  24
n₃ =  12

Step-by-step explanation:

$$\begin{gathered} \frac{n}{3}+\frac{4}{9}n+12=n \\ n/3+4/9\cdot n+12=n \\ 2n=108 \\ n=\frac{108}{2}=54 \\ n=54 \end{gathered}$$

$n_1=n/3=54/3=18$

$n_2=4/9n=4/9\cdot 54=24$

$n_3=12$

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