Question

Alfa numerele a.b.c,stiind ca a+b=300,,b+c=500,irá a+c=400

Answer 1

adunam relatiile: 2a+2b+2c=1200, deci: a+b+c=600:
c=600-300=300
a=400-300=100
b=300-100=200

Answer 2

$\displaystyle a+b=300 \\ b+c=500 \\ a+c=400 \\ a+b+b+c+a+c=300+500+400 \Rightarrow 2a+2b+2c=1200 \Rightarrow \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \Rightarrow 2(a+b+c)=1200 \Rightarrow a+b+c= \frac{1200}{2} \Rightarrow \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{a+b+c=600} \\ 300+c=600 \Rightarrow c=600-300 \Rightarrow \boxed{c=300} \\ a+500=600 \Rightarrow a=600-500 \Rightarrow \boxed{a=100} \\ a+b=300 \Rightarrow 100+b=300 \Rightarrow b=300-100 \Rightarrow \boxed{b=200}$
$Verificare:100+200+300=\boxed{600}$