Question

Victor,Andrei si Ionut au impreuna 950 de lei.Dupa ce Victor cheltuieste in excursie 25%,Andrei 40%,iar Ionut 70% au observat ca le-au ramas sume egale.Ce suma a avut fiecare copil?

Answer 1

a+b+c=950
(75%)a=(60%)b=(30%)c
75a/100=60b/100=30c/100

75a=60b=30c:5⇒  invers proportionale
15a=12b=6c=k⇒a=k/15,  b=k/12  si c=k/6
a+b+c=950
a+b+c=k/15+k/12+k/6=950
12×6×k+15×5×k+15×13×k=950×12×15×6
72k+75k+195k=950×12×15×6
342k=950×12×15×6
k=3000
a=k/15=200  Victor are 200 lei
b=k/12=250  Andrei  250 lei
c=k/6=500    Ionut 500 lei

Verificare
a+b+c=950
200+250+500=950
950=950