Question

Suma a doua numere este 1400.Afla numerele stiind ca diferenta lor este cat a treia parte din numarul mai mic.Care sunt numerele?

Answer 1

$\left \{ {{a+b=1400} \atop {b-a= \frac{a}{3} /(*3)}} \right.$  ⇔  $\left \{ {{a+b=1400} \atop {3b-3a=a}} \right.$  ⇔  $\left \{ {{a+b=1400} \atop {3b=4a}} \right.$  ⇔  $\left \{ {{a+b=1400} \atop {b= \frac{4a}{3} }} \right.$  ⇔  $\left \{ {{a+\frac{4a}{3}=1400/(*3) } \atop {b= \frac{4a}{3}} \right.$  ⇔ 
${{\left \{ {{3a+4a=4200} \atop {b= \frac{4a}{3} }} \right.$  ⇔  $\left \{ {{7a=4200} \atop {b= \frac{4a}{3} }} \right.$  ⇔  $\left \{ {{a=600} \atop {b= \frac{4*600}{3} }} \right.$  ⇔  $\left \{ {{a=600} \atop { b=\frac{2400}{3} }} \right.$  ⇔  $\left \{ {{a=600} \atop {b=800}} \right.$

Proba:

a+b=1400
600+800=1400
1400=1400

b-a=a/3
800-600=600/3
200=200