Question

Tìm ba số x, y , z, biết rằng: \(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\) và x + y - z= 10.

 

Answer 1

Ta có x/8=y/12=z/15

Theo t/c của dãy tỉ số bằng nhau , ta có

x/8=y/12=z/15=x+y-z/8+12-15=10/5=2

x/2=2 , x=4

Answer 2

Ta cóx/2=y/3;y/4=z/5

=>x/8=y/12=z/15

Áp dụng t/c của dãy tỉ số bằng nhau ta có:

x/8=y/12=z/15=x+y-z/8+12-15=10/5=2

=> x=16,y=24,z=30

Answer 3

\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}=>\frac{x}{8}=\frac{y}{12};\frac{y}{12}=\frac{z}{15}\)

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)

Nên x = 2.8 = 16

      y = 2.12 = 24

      z= 2. 15 = 30

 

Answer 4

\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\)

\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{1}{4}.\frac{x}{2}=\frac{1}{4}.\frac{y}{3}=\frac{x}{8}=\frac{y}{12}\)

\(\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{1}{3}.\frac{y}{4}=\frac{1}{3}.\frac{z}{5}=\frac{y}{12}=\frac{z}{15}\)

Áp dụng tính chất DTS bằng nhau: 

   \(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\Rightarrow\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)

\(\frac{x}{8}=2\Rightarrow x=2.8=16\)

\(\frac{y}{12}=2\Rightarrow y=2.12=24\)

\(\frac{z}{15}=2\Rightarrow z=2.15=30\)

Vậy...

Answer 5

\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{12}\)(1)

\(\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{15}\)(2)

Từ (1) và (2) \(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)

Đặt \(\frac{x}{8}=\frac{y}{12}=\frac{z}{18}\)= k => x = 8k ; y = 12k ; z = 15k 

x + y - z = 10 => 8k + 12k - 15k = 10 => 5k = 10 => k = 2 

Do đó : 

\(\frac{x}{8}=2\Rightarrow x=2.8=16\)

\(\frac{y}{12}=2\Rightarrow y=2.12=24\)

\(\frac{z}{15}=2\Rightarrow z=2.15=30\)

Vậy ... 

Answer 6

x/8=y/12=z/15=x+y-z/8+12+15=10/5=2

x=16,y=24,z=30

Answer 7

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}\)=2

\(\frac{x}{8}\)= 2 => x = 2.8 = 16

\(\frac{y}{12}\)= 2 => y = 12.2 = 24

\(\frac{z}{15}\)= 2 => z = 15.2 = 30

Vậy x = 16, y = 24, z = 30