Question

Se stie ca a/b=5/3. Determinati numerele a si b, stiind ca: a) a-b=76 b) a+b=168 c) 2a+5b=150 d) 4a+2b=260

Answer 1

[tex]\frac{a}{b}=\frac{5}{3}, 3a=5b(1).\\ a).a-b=76|\cdot 3, 3a-3b=228, din(1) 5b-3b=228, 2b=228, b=114\\ a=76+b=114+76=190.\\ b).a+b=168|\cdot 3, 3a+3b=504, din (1) 5b+3b=504, 8b=504, b=63\\ a=168-b=168-63=105\\ c).2a+5b=150, din (1) 2a+3a=150, 5a=150, a=50,\\ 3a=5b, \\150=5b, b=30\\ d).4a+2b=260|:2, 2a+b=130|\cdot 5, 10a+5b=130\cdot 5, din(1)\\13a=130\cdot 5, a=50,\\ 2a+b=130, 100+b=130, b=30[/tex]