Question

1) impartiti numarul 120 in trei parti direct propotionale cu 4.5 si 11
2)Cassian a cheltuit80% dintr-o suma de bani si apoi20%din cat cheltuit prima data .Daca i-au ramas 15 lei ,aflati suma initiala a lui Cassian

Answer 1

1) Fie a,b,c partile si avem:

{a,b,c} dp {4,5,11}

a=4k

b=5k

c=11k

a+b+c=120

4k+5k+11k=120

20k=120

k=6

a=4*6=24

b=5*6=30

c=11*6=66

2)

Fie x suma initiala.

80% din x=80x/100=4x/5 -prima suma cheltuita

20% din 4x/5=20/100*4x/5=1/5*4x/5=4x/(5*5)=4x/25 - a doua suma cheltuita

4x/5+4x/25=(5*4x+4x)/25=24x/25 - suma cheltuita in total

x-24x/25=x/25 - suma ramasa (cea care valoreaza 15 lei)

x/25=15

x=25*15

x=375 lei

Cassian a avut initial 375 lei.