Pupils - boys and girls

5/8 of the pupils in a hall were boys. 7/10 of the boys wore glasses. 48 boys didn't wear glasses. How many pupils were there in the hall?

Correct answer:

n =  256

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{5}{8}=0.625 \\ {q}_1=r_1\cdot \frac{7}{10}=\frac{5}{8}\cdot \frac{7}{10}=\frac{5\cdot 7}{8\cdot 10}=\frac{35}{80}=\frac{7}{16}=0.4375 \\ {q}_2=r_1\cdot \frac{10-7}{10}=\frac{5}{8}\cdot \frac{10-7}{10}=\frac{3}{16}=0.1875 \\ 48=n\cdot q_2 \\ n=48/q_2=48/\frac{3}{16}=48:\frac{3}{16}=48\cdot \frac{16}{3}=\frac{48\cdot 16}{3}=\frac{768}{3}=256 \end{gathered}$$

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