已知(x+1)/2=(y+3)/4=(x+y)/5,求代数式(3x+2y+1)/(x+2y+3)的值

已知(x+1)/2=(y+3)/4=(x+y)/5,求代数式(3x+2y+1)/(x+2y+3)的值
已知(x+1)/2=(y+3)/4=(x+y)/5,求代数式(3x+2y+1)/(x+2y+3)的值

已知(x+1)/2=(y+3)/4=(x+y)/5,求代数式(3x+2y+1)/(x+2y+3)的值
设(x+1)/2=(y+3)/4=(x+y)/5=K,
则X+1=2K,X=2K-1,
Y+3=4K,Y=4K-3,
X+Y=5K,
∴(2K-1)+(4K-3)=5K,
K=4,
∴X=7,Y=13,
∴(3x+2y+1)/(x+2y+3)
=(21+26+1)/(7+26+3)
=48/36
=4/3

原式等价于10(x+1)=5(y+3)=4(x+y)
10(x+1)=5(y+3)，可得2x-y=1
5(y+3)=4(x+y)，可得4x-y=15
解得x=7，y=13
x+2y+3=36 3x+2y+1=48
两式相除48/36，得0.75