Answer:
y = 1
Step-by-step explanation:
We convert the numbers from the binary system to a decimal system:
[tex]101_2=1\cdot2^2+0\cdot2^1+1\cdot2^0=4+0+1=5_{10}\\\\11_2=1\cdot2^1+1\cdot2^0=2+1=3_{10}\\\\10010_2=1\cdot2^4+0\cdot2^3+0\cdot2^2+1\cdot2^1+0\cdot2^0=16+0+0+2+0=18_{10}[/tex]
Therefore we have
[tex]\dfrac{y_2}{y_2+101_2}=\dfrac{11_2}{10010_2}\Rightarrow\dfrac{y}{y+5}=\dfrac{3}{18}\qquad\text{cross multiply}\\\\18y=3(y+5)\qquad\text{use the distributive property}\\\\18y=3y+15\qquad\text{subreact}\ 3y\ \text{from both sides}\\\\15y=15\qquad\text{divide both sides by 15}\\\\y=1_{10}\Rightarrow y_2=1\cdot2^0=1_2[/tex]
