Question

numa sala de aula 1/3 dos alunos preferem futebol 1/4 vôlei e os 20 restantes basquete quantos alunos tem nessa sala

Answer 1

Considerando o numero total de alunas da sala sendo $\mathsf{n}$. Logo:

$\mathsf{\dfrac{n}{3}+\dfrac{n}{4}+20=n}\\\\\\\mathsf{\dfrac{4\cdot n}{4\cdot 3}+\dfrac{3\cdot n}{3\cdot 4}+20=n}\\\\\\\mathsf{\dfrac{4n}{12}+\dfrac{3n}{12}+20=n}\\\\\\\mathsf{\dfrac{4n+3n}{12}+20=n}\\\\\\\mathsf{n=20+\dfrac{7n}{12}}\\\\\\\mathsf{n-\dfrac{7n}{12}=20}\\\\\\\mathsf{\dfrac{12n}{12}-\dfrac{7n}{12}=20}\\\\\\\mathsf{\dfrac{12n-7n}{12}=20}\\\\\\\mathsf{5n=20\cdot 12}\\\\\mathsf{n=\dfrac{5\cdot 4\cdot 12}{5}}\\\\\\\boxed{\mathsf{n=48\: alunos}}\: \: \checkmark$