a) notam cu a,b,c sumele de bani primite de cei trei frati
Din problema deducem relatia urmatoare (am efectuat si cateva simplificari pt a usura calculele)
[tex]a- \frac{2}{3} a=b - \frac{3}{4} b=c- \frac{2}{5}c \\ \frac{a}{3} = \frac{b}{4}= \frac{3c}{5} \\ a* \frac{1}{3} =b* \frac{1}{4} =c* \frac{3}{5} =k \\ a= \frac{k}{ \frac{1}{3} } , b=\frac{k}{ \frac{1}{4} } , c = \frac{k}{ \frac{3}{5} } \\ a=3k ,b=4k,c= \frac{5k}{3} \\ a+b+c=130 \\ 3k+4k+ \frac{5k}{3} =130 \\ \frac{9k+12k+5k}{3} = 130 \\ \frac{26k}{3} =130 \\ 26k=130*3 \\ 26k=390 \\ k=390 :26 \\ k=15 \\ a=15*3=45 \\ b=4*15=60 \\ c= \frac{5*15}{3} =25[/tex]
b) Fiecare frate a cheltuit:
[tex]\frac{2}{3} a= \frac{2*45}{3} =30 (lei) \\ \frac{3}{4} b= \frac{3*60}{4}=45(lei) \\ \frac{2}{5} c= \frac{2*25}{5} =10(lei)[/tex]
