Question

\(\dfrac{x}{3}\)=\(\dfrac{y}{5}\)=\(\dfrac{z}{2}\)và 5x-y+3z=124

Answer 1

Ta có: \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{2}\)

nên \(\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{6}\)

mà 5x-y+3z=124

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{6}=\dfrac{5x-y+3z}{15-5+6}=\dfrac{124}{16}=\dfrac{31}{4}\)

Do đó: \(\left\{{}\begin{matrix}x=\dfrac{93}{4}\\y=\dfrac{165}{4}\\z=\dfrac{31}{2}\end{matrix}\right.\)

Answer 2

Ta có:

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{2}=\dfrac{5x}{15}=\dfrac{3z}{6}=\dfrac{5x-y+3z}{15-5+6}=\dfrac{124}{16}=\dfrac{31}{4}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{31}{4}.3=\dfrac{93}{4}\\z=\dfrac{31}{4}.2=\dfrac{31}{2}\\y=\dfrac{31}{4}.5=\dfrac{155}{4}\end{matrix}\right.\)

Answer 3

x/3 = y/5 = z/2 = 5x/15 =y/5 = 3z/6 = 5x -y + 3z / 15 -5 + 6 = 124/16 =31/4

x = 31/4 . 3 = 93/4 

y = 31/4 . 5 = 155/4 

z = 31/4 . 2 =31/2