Question

Intr-o urna se gasesc un numar de bile albe, bile negre si bile rosii direct proportionale cu 2, 3, 7.
a) daca in total sunt 60 bile aflati nr de bile rosii
b) daca nr de bile negre este egal cu x+1, x € N aflati nr total de bile in functie de nr natural x.

Answer 1

a) a+n+r=60
a/2=n/3=r/7=k; a=2k, n=3k, r=7k
2k+3k+7k=60 ⇒ 12k=60 ⇒ k=5
a=2k=10 bile albe
n=3k=15 bile negre
r=7k=35 bile rosii
b) n=x+1=3k ⇒ k=(x+1)/3 ⇒ a=2k=2(x+1)/3, r=7k=7(x+1)/3
a+n+r=2(x+1)/3 + 3(x+1)/3 + 7(x+1)/3=(12x+12)/3=4x+4=4(x+1)

Answer 2

a. a/2=n/3=r/7=k
⇒a/2=k
⇒a=2k;
⇒n/3=k
⇒n=3k;
⇒r/7=k
⇒r=7k;
a+n+r=60
⇒2k+3k+7k=60
⇒12k=60
⇒k=60/12
⇒k=5;
⇒r=7k
⇒r=7·5⇒r=35[bile rosii];