Question

Tìm x,y,z,t biết{x+y+z+t=12

x:y:z:t=3:5:7:9

Answer 1

x : y : z : t = 3 : 5 : 7 : 9 mà x + y + z + t = 12;

=> Theo tính chất dãy tỉ số bằng nhau, ta có:

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{t}{9}\)

=> \(\dfrac{x+y+z+t}{3+5+7+9}\) = \(\dfrac{12}{24}=0,5.\)

Suy ra:

x = 0,5 . 3 = 1,5;

y = 0,5 . 5 = 2,5;

z = 0,5 . 7 = 3,5;

t = 0,5 . 9 = 4,5.

Vậy x = 1,5, y = 2,5, z = 3,5, t = 4,5.

Answer 2

Ta có: x:y:z:t=3:5:7:9

suy ra \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{t}{9}\)

Mà x + y + z + t = 12 ( theo đề bài )

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{t}{9}=\dfrac{x+y+z+t}{3+5+7+9}\)

= \(\dfrac{12}{24}=\dfrac{1}{2}\)

+) \(\dfrac{x}{3}=\dfrac{1}{2}\) suy ra x = \(\dfrac{3}{2}\)

+) \(\dfrac{y}{5}=\dfrac{1}{2}\) suy ra y = \(\dfrac{5}{2}\)

+) \(\dfrac{z}{7}=\dfrac{1}{2}\) suy ra z = \(\dfrac{7}{2}\)

+) \(\dfrac{t}{9}=\dfrac{1}{2}\) suy ra t = \(\dfrac{9}{2}\)

Vậy x = \(\dfrac{3}{2}\) ; y = \(\dfrac{5}{2}\) ; \(z=\dfrac{7}{2};t=\dfrac{9}{2}\)