Question

Mihai avea o suma de bani.In prima zi cheltuie 2/6 din suma, a doua zi 3/4 din rest, in a treia zi 3/5 din noul rest, ramanandu-i 16 lei.Câți lei a avut la inceput si câți lei a cheltuit in fiecare zi?

Answer 1

Fie:a-suma de bani._________________ _I zi:a•2/6=a/3._____________________ _IIzi:(a-a•/3)•3/4=(3a/3-a/3)•3/4=2a/3•3/4=6a/12=a/2._____ _IIIzi:(a-a/3-a/2)•3/5=(6a/6-2a/6-3a/6)•3/5=a/6•3/5=3a/30=a/10. Si mai ramane cu 16 lei._____________ ___a=Izi+IIzi+IIIzi+16lei______________ ___a=a/3+a/2+a/10+16lei_____________ ___a=10a/30+15a/30+3a/10+16lei_____ ___a=28a/30+16lei__________________ ___=>a-28a/30=16lei_______________ ___=>a-14a/15=16lei________________ ___=>15a/15-14a/15=16lei___________ ___=>a/15=16lei_=>a=16•15=240.