Alien currency

Answer: $19$

Elimination multiplying equations by $3$ and $8$

               $$$\begin{array}{rl}3g+8b=46\Rightarrow & 24g+64b=368\\ 8g+3b=31\Rightarrow & \underset{―}{24g+9b=93}\\ \text{subtracting gives:}& 55b=275\\ & \Rightarrow 11b=55\\ & \Rightarrow b=5\end{array}$$$

And so $3g+40=46\Rightarrow g=2$

$\therefore 2g+3b= 4+15=19$

Elimination by combining equations more than once

$$\begin{array}{rl}3g+8b=46& \\ \underset{―}{+8g+3b=31}& \\ 11g+11b=77& \\ \Rightarrow g+b=7& \\ \Rightarrow 3g+3b=21\end{array}$$

                     $$$\begin{array}{rl}3g+8b=46& \\ \underset{―}{-3g+3b=21}& \\ 5b=25& \\ \Rightarrow b=5& \end{array}$$$              $$$\begin{array}{rl}8g+83=31& \\ \underset{―}{-3g+3b=21}& \\ 5g=10& \\ \Rightarrow g=2& \end{array}$$$

Therefore $2g + 3b = 19$.

Getting $2g+3b$ without finding $g$ and $b$

$$$\begin{array}{rl}3g+8b=46& \\ \underset{―}{+8g+3b=31}& \\ 11g+11b=77& \\ \Rightarrow g+b=7& \end{array}$$$

        $3g+8b$

$+ \quad (\ g\ +\ b\ )\times$ some    to get blues and greens in ratio $2:3$

                                    difference will be $5$ since $8$ and $3$ have difference of $5$

                                    $10:15 = 3+7:8+7$

$$$\begin{array}{rl}3g+8b=46& \\ \underset{―}{+7g+7b=49}& \\ 10g+15b=95& \\ \Rightarrow 2g+3b=19& \end{array}$$$