Question

Fie proportia(3a-b)/(2a+b)=1/2.
a)Sa se afle valoarea raportului a/b.
b)Sa se afle cite procente reprezinta numarul a-b din numarul 2a+b.

Answer 1

a)
(3a-b)/(2a+b)=[b(3a/b -1)]/[b(2a/b +1)]=(3a/b -1)/(2a/b +1), notam a/b=t
(3a-b)/(2a+b)=1/2
(3t-1)/(2t+1)=1/2
2(3t-1)=2t+1
6t-2=2t+1
4t=3
t=3/4
a/b=3/4
b)
a/b=3/4=>4a=3b=>a=3b/4
3a-b=9b/4-b=5b/4
2a+b=6b/4+b=3b/2+b=5b/2
(5b/4)/(5b/2)x100%=(2/4)x100%=(1/2)x100%=50%