VA ROG AJUTATIMA DAU COROANA EX 15 VA ROOOOG

Notez cu a si b numerele.
a>b;

a:b=5 rest 9=>a=5b+9;

La b se adauga 3: b+3;

a:(b+3)=4 rest 15=>a=4(b+3)+15;
a=4b+12+15=4b+27;

Avem: a=5b+9
Si a=4b+27
Din ambele => 5b+9=4b+27;
5b-4b=27-9;
b=18 => a=5×18+9=90+9=99;

Raspuns: Numerele sunt 99 si 18.

Verificare: 99:18=5 rest 9;
99:(18+3)=99:21=4 rest 15.

Answer Link

Tcostel Tcostel · Answer 2 · 2017-09-14T07:38:44+03:00

[tex]\begin{cases} x:y=5\text{ rest }9\\ x:(y+3)=4\text{ rest }15 \end{cases}\\\\\\ \begin{cases} x=5y+9\\ x=4(y+3)+15 \end{cases}\\\\\\ \begin{cases} x=5y +9\\ x= 4y+12+15 \end{cases}\\\\\\ \begin{cases} x-5y=9~~~|\cdot(-1)\\ x-4y=27 \end{cases}\\\\\\ \begin{cases} -x+5y=-9\\ x-4y=27 \end{cases}~\text{(Adunam ecuatiile)}\\\\\\ ~~~/~~~~~y=\boxed{18}\\\\ x=4y+27=4\cdot18+27=72+27=\boxed{99}\\\\ \text{Solutia:}\displaystyle\\\\ \boxed{\bf \left{{x=18}\atop{y=99}}\right} [/tex]