Question

Sa se afle valoarea numerelor a,b,c, știind că :

a+b=30

a+c=40

b+c=50

Answer 1

a+b+a+c+b+c=30+40+50
2a+2b+2c=120
a+b+c=60
c=60-30=30
a=60-50=10
b=60-40=20

Answer 2

$\displaystyle a+b=30 \\ a+c=40 \\ b+c=50 \\ a+b+a+c+b+c=30+40+50 \Rightarrow 2a+2b+2c=120 \Rightarrow \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow2(a+b+c)=120 \Rightarrow a+b+c= \frac{120}{2} \Rightarrow \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{a+b+c=60} \\ a+b+c=60 \Rightarrow 30+c=60 \Rightarrow c=60-30 \Rightarrow \boxed{c=30} \\ a+c=40 \Rightarrow a+30=40 \Rightarrow a=40-30 \Rightarrow \boxed{a=10}$
$b+c=50 \Rightarrow b+30=50 \Rightarrow b=50-30 \Rightarrow \boxed{b=20} \\ Verificare : 10+20+30=30+30=\boxed{60}$