Department 82388

Last year, there were 30 more boys than girls in our scout troop. This year, the number of children in the ward increased by 10%, while the number of boys increased by 5% and the number of girls increased by 20%. How many children do we have in the department this year?

Correct answer:

n =  99

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+10\%=1+\frac{10}{100}=1.1 \\ {r}_2=100\%+5\%=1+\frac{5}{100}=1.05 \\ {r}_3=100\%+20\%=1+\frac{20}{100}=1.2 \\ a=30+b \\ {r}_1\cdot (a+b)=r_2\cdot a+r_3\cdot b \\ {r}_1\cdot ((30+b)+b)=r_2\cdot (30+b)+r_3\cdot b \\ 1.1\cdot ((30+b)+b)=1.05\cdot (30+b)+1.2\cdot b \\ 0.05b=1.5 \\ b=\frac{1.5}{0.05}=30 \\ b=30 \\ a=30+b=30+30=60 \\ n=1.1\cdot (a+b)=1.1\cdot (60+30)=99 \end{gathered}$$

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