Notăm sumele celor doi copii cu a și b.
[tex]\it a+b=64\ \ \ \ (*)\\ \\ \dfrac{3}{4}\cdot a=\dfrac{4}{5}\cdot b \Rightarrow \dfrac{3a}{4}=\dfrac{4b}{5}\Rightarrow 15a=16b|_{+16a} \Rightarrow 31a=16a+16b \Rightarrow\\ \\ \Rightarrow31a=16(a+b)\ \stackrel{(*)}{\Longrightarrow}\ 31a=16\cdot124|_{:31} \Rightarrow a=16\cdot4 \Rightarrow a=64\\ \\ a=64\ \stackrel{(*)}{\Longrightarrow} 64+b=124 \Rightarrow b=60[/tex]
Prin urmare, primul elev are 64 de lei, iar al doilea elev are 60 de lei.
