School reward

There were 560 pupils in the school. They rewarded 8% of all boys and 10% of all girls for excellent results. The directorate stated that teachers rewarded 9% of all pupils. How many boys and how many girls attended the school?

Final Answer:

a =  280
b =  280

Step-by-step explanation:

$$\begin{gathered} r_1=8\%=\frac{8}{100}=\frac{2}{25}=0.08 \\ {r}_2=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ {r}_3=9\%=\frac{9}{100}=0.09 \\ a+b=560 \\ {r}_1\cdot a+r_2\cdot b=r_3\cdot 560 \\ {r}_1\cdot a+r_2\cdot (560-a)=r_3\cdot 560 \\ 0.08\cdot a+0.1\cdot (560-a)=0.09\cdot 560 \\ 0.02a=5.6 \\ a=\frac{5.6}{0.02}=280 \\ a=280 \end{gathered}$$

$b=560-a=560-280=280$

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