Question

Raportul a doua numere este 3/2. Jumătate din suma numerelor, mărită cu 30, este egala cu 450. Aflati numerele.

Answer 1

$\frac{x}{y} = \frac{3}{2} = > x = \frac{3y}{2} \\ \\ \frac{x \: + \: y}{2} \: + \: 30 = 450 \\ \\ \frac{ \frac{3y}{2} \: + \: ^{2)} y }{2} + 30 = 450 \\ \\ \frac{ \frac{3y}{2} \: + \: \frac{2y}{2} }{2} \: + \: 30 = 450 \\ \\ \frac{ \frac{3y \: + \: 2y}{2} }{2} = 450 \: - \: 30 \\ \\ \frac{ \frac{5y}{2} }{2} = 420 \\ \\ \frac{5y}{2} \cdot \frac{1}{2} = 420 \\ \\ \frac{5y}{4} \: = \: ^{4)} 420 \\ \\ 5y = 1680 \\ \\ y = \frac{1680}{5} \\ \\ y = 336 \\ \\ x = \frac{3 \cdot 336}{2} \\ \\ x = 504$

Answer 2

a/b = 3/2 ⇒ b = 2a/3
a+b  /  2    +    30 = 450
a+b / 2 = 420
a+b = 840
a+2a/3 = 840
5a = 3*840 l :5
a = 3*168 = 504
b = 2*504 / 3 = 2*168 = 336.
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