Question

S-au cumparat 3 caiete si 5 truse de geometrie cu 142 lei .pentru 3 caiete s-a platit cu 2 lei mai mult decat pentru doua truse . Determinati pretul unui caiet si pretul unei truse .

Answer 1

3c+5t=142 lei
3c=2t+2
2t+2+5t=142
7t=142-2=140
t=140/7=20
3c+100=142
3c=42
c=42/3=14

Answer 2

x-prețul unui caiet
y-prețul unei truse de geometrie

$\left \{ {{3x+5y=142} \atop {3x-2=2y}} \right.⇔ \left \{ {{3x=142-5y} \atop {142-5y-2=2y}} \right.⇔ \left \{ {{3x=142-5y} \atop {-5y-2y=-142+2}} \right.⇔ \left \{ {{3x=142-5y} \atop {-7y=-140}} \right. ⇔ \left \{ {{3x=142-5y} \atop {7y=140}} \right.⇔$$\left \{ {3x=142-5y} \atop {y=20}} \right. ⇔ \left \{ {{3x=142-5*20} \atop {y=20}} \right. ⇔ \left \{ {{3x=142-100} \atop {y=20}} \right.⇔ \left \{ {{3x=42} \atop {y=20}} \right. ⇔ \left \{ {{x=42:3} \atop {y=20}} \right. ⇔ \left \{ {{x=14} \atop {y=20}} \right.$
3·14+5·20=42+100=142 (A)
Raspuns: x=14, y=20.