SAT Question b8e73b5b: Linear Inequalities answer and explanation with Desmos solution

Choice C is correct. Ken earned $$8$ per hour for the first $10$ hours he worked, so he earned a total of $$80$ for the first $10$ hours he worked. For the rest of the week, Ken was paid at the rate of $$10$ per hour. Let $x$ be the number of hours he will work for the rest of the week. The total of Ken's earnings, in dollars, for the week will be $10x+80$. He saves $90\%$ of his earnings each week, so this week he will save $0.9\times (10x+80)$ dollars. The inequality $0.9\times (10x+80)\ge 270$ represents the condition that he will save at least $$270$ for the week. Factoring $10$ out of the expression $10x+80$ gives $10\times (x+8)$. The product of $10$ and $0.9$ is $9$, so the inequality can be rewritten as $9\times (x+8)\ge 270$. Dividing both sides of this inequality by $9$ yields $x+8\ge 30$, so $x\ge 22$. Therefore, the least number of hours Ken must work the rest of the week to save at least $$270$ for the week is $22$.