已知x、y的值满足等式(x+1)/2=(y+3)/4=(x+y)/5,求式子(3x+2y+1)/(x+2y+3)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 17:24:55
已知x、y的值满足等式(x+1)/2=(y+3)/4=(x+y)/5,求式子(3x+2y+1)/(x+2y+3)的值

已知x、y的值满足等式(x+1)/2=(y+3)/4=(x+y)/5,求式子(3x+2y+1)/(x+2y+3)的值
已知x、y的值满足等式(x+1)/2=(y+3)/4=(x+y)/5,求式子(3x+2y+1)/(x+2y+3)的值

已知x、y的值满足等式(x+1)/2=(y+3)/4=(x+y)/5,求式子(3x+2y+1)/(x+2y+3)的值
(x+1)/2=(x+y)/5 (1)
(y+3)/4=(x+y)/5 (2)
由(1)得
5x+5=2x+2y
3x-2y=-5 (3)
由(2)得
5y+15=4x+4y
4x-y=15 (4)
(3)-(4)×2得
-5x=-35
∴x=7
把x=7代入(3)得
y=13

(3x+2y+1)/(x+2y+3)
=(21+26+1)/(7+26+3)
=48/36
=4/3

(x+1)/2=(y+3)/4=(x+y)/5=t
x=2t-1
y=4t-3
x+y=5t

6t-4=5t
t=4
所以
x=7,y=13
从而
(3x+2y+1)/(x+2y+3)
=(21+26+1)/(7+26+3)
=48/36
=4/3