$a$) `x/{15} = y/{20} = z/{28}`
`⇔ {2x}/{30} = {3y}/{60} = z/{28}`
$2x+3y-2 = 186$
$⇔ 2x + 3y = 188$
`⇔ {2x}/30 = {3y}/60 = z/{28} = {2x+3y}/30+60 = 188/90 = 94/45`
$⇒$ $⇒$ $\left\{\begin{matrix}x=\dfrac{94}{3}& \\y=\dfrac{376}{9}& \\z =\dfrac{2632}{45}& \end{matrix}\right.$
Vậy `(x;y;z)=(94/3;376/9;2632/45}`.
$b$) `{x-3}/{x+5} = 5/7`
`⇔ 5.(x+5) = 7.(x-3)`
`⇔ 5x+25 = 7x -21`
`⇔ 25 +21 = 7x - 5x`
`⇔ 46 = 2x`
`⇔ x = 23`
Vậy `x=23`.
$c$) `x/4 = y/3 = z/9`
`⇔ x/4 = {3y}/9 = {4z}/36`
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
`x/4 = {3y}/9 = {4z}/36 = {x-3y+4y}/{4-9+36} = 62/31= 2`
`⇒` $⇒$ $\left\{\begin{matrix}x=8& \\y=6& \\z = 18& \end{matrix}\right.$
Vậy `(x;y;z)=(8;6;18)`.
