Question

1.Suma a patru numere este 345. Aflati numerele stiind ca al doilea este 80% din primul,al treilea este trei sferturi din al doilea si al patrulea este 3 supra 5 din al treilea.
2. Intr-o clasa sunt 28 de elevi. Aratati ca exista cel putin trei elevi nascuti in aceeasi luna a anului.

Answer 1

1) a+b+c+d=345
b=80a/100=8a/10=4a/5
c=3/4x4a/5=3a/5
d=3/5x3a/5=9a/25
a+4a/5+3a/5+9a/25=345
(25a+20a+15a+9a)/25=345
69a=345x25
a=8625/69
a=125
c=3a/5=(3x125)/5=75
c=75
b=4a/5=(4x125)/5=100
b=100
d=9a/25=(9x125)/25=45
d=45

verificare
125+100+75+45=345

Answer 2

a,b,c,d cele 4 numere
a+b+c+d=345
b=80% din a
b=ax 80/100=80a/100=8a/10=4a/5
b=4a/5 =>5b=4a =>a=5b/4
c=3b/4
d=3c/5 =>d=3x(3b/4)/5=9b/4/5=9b/4 x1/5=9b/20
d=9b/20
a+b+c+d=345
5b/4+b+3b/4+9b/20=345
aducem la acelasi numitor
25b/20 +20b/20+15b/20+9b/20=345
69b/20=345
69 b=345 x20
69 b=6900
b=6900/69
b=100
a=25b/20=2500/20=125
c=15b/20=1500/20=75
d=9b/20=900/20=45
a=100,b=125,c=75,d=45