SAT Question 107d0c62: Linear Equations In Two Variables answer and explanation with Desmos solution

It’s given that the equation $0.10x+0.20y=0.17(x+y)$ represents mixing a $10\%$ solution and a $20\%$ solution to obtain a $17\%$ solution. It’s also given that $x$ represents the volume, in gallons, of the $10\%$ solution. If $90.0$ gallons of the $10\%$ solution is used, it follows that $x=90.0$. Substituting $90.0$ for $x$ in the given equation yields $0.10(90.0)+0.20y=0.17(90.0+y)$, or $9+0.20y=15.3+0.17y$. Subtracting $0.17y$ from both sides of this equation yields $9+0.03y=15.3$. Subtracting $9$ from both sides of this equation yields $0.03y=6.3$. Dividing both sides of this equation by $0.03$ yields $y=210$. Therefore, the volume of the $20\%$ solution that could be mixed with $90.0$ gallons of the $10\%$ solution to produce a $17\%$ solution is $210$ gallons.