Question

gastei 2/3 do dinheiro do meu salario e depois gastei 1/4 do restante, ficando com R$ 120,00 apenas. meu salario e de:

Answer 1

$\frac{2}{3} \ x \ + \ \frac{1}{4} \ (x \ - \ \frac{2}{3} \ x ) \ = \ x \ - \ 120 \\ \\ mmc \ (1, \ 3) \ = \ 3 \\ \\ \frac{2x}{3} \ + \ \frac{1}{4} \ (\frac{3x \ - \ 2x}{3}) \ = \ x \ - \ 120 \\ \\ \frac{2x}{3} \ + \ \frac{3x \ - \ 2x}{12} \ = \ x \ - \ 120 \\ \\ mmc \ (3, \ 12) \ = 12 \\ \\ 8x \ + \ 3x \ - \ 2x \ = \ 12x \ - \ 1440$

$8x \ + \ 3x \ - \ 2x \ - \ 12x \ = \ - \ 1440 \\ \\ - \ 3x \ = \ - \ 1440 \\ \\ x \ = \ - \ 1440 \ \div \ (- \ 3) \\ \\ x \ = \ 480 \\ \\ Resposta: \ R\ \ 480,00$

Answer 2

$\sf \displaystyle \frac{2}{3}x+\frac{1}{4}\left(x-\frac{2}{3}x\right)=x-120\\\\\\\frac{2}{3}x+\frac{x-\frac{2}{3}x}{4}=x-120\\\\\\{Multiplicar\:pelo\:m\acute{i}nimo\:m\acute{u}ltiplo\:comum=}12\\\\\\\frac{2}{3}x\cdot \:12+\frac{x-\frac{2}{3}x}{4}\cdot \:12=x\cdot \:12-120\cdot \:12\\\\\\9x=x\cdot \:12-1440\\\\\\9x-x\cdot \:12=x\cdot \:12-1440-x\cdot \:12\\\\\\-3x=-1440\\\\\\\frac{-3x}{-3}=\frac{-1440}{-3}\\\\\\\to \boxed{\sf x=R\ 480}$