jmc

First, we find the probability both are green, then the probability both are blue, and add the two probabilities. The sum should be equal to $0.58$. The probability both are green is $\frac{4}{10}\cdot \frac{16}{16+N}$, and the probability both are blue is $\frac{6}{10}\cdot \frac{N}{16+N}$, so$$\frac{4}{10}\cdot \frac{16}{16+N}+\frac{6}{10}\cdot \frac{N}{16+N}=\frac{29}{50}$$Solving this equation,$$20\left(\frac{16}{16+N}\right)+30\left(\frac{N}{16+N}\right)=29$$Multiplying both sides by $16+N$, we get$$20\cdot 16+30\cdot N=29(16+n)\Rightarrow 320+30N=464+29N\Rightarrow N=\boxed{144}$$