A student earns $$ \$ 12 $$ per hour at a grocery store and $$ \$ 16 $$ an hour cleaning. The student must work at least 10 hours a week at the grocery store. The student also works no more than 20 hours a week and wants to earn at least 8240 each week. Which system of inequalities represents the number of hours, $$ x $$, worked at the grocery store and the number of hours, $$ y $$ worked cleaning? A. $$ 12 x+16 y \leq 240, x10, x+y10, x+y

Question

A student earns $$ \$ 12 $$ per hour at a grocery store and $$ \$ 16 $$ an hour cleaning. The student must work at least 10 hours a week at the grocery store. The student also works no more than 20 hours a week and wants to earn at least 8240 each week. Which system of inequalities represents the number of hours, $$ x $$, worked at the grocery store and the number of hours, $$ y $$ worked cleaning? A. $$ 12 x+16 y \leq 240, x>10, x+y<20 $$ B. $$ 12 x+16 y \geq 240, x>10, x+y<20 $$ C. $$ 12 x+16 y \leq 240, x \geq 10, x+y \leq 20 $$ D. $$ 12 x+16 y \geq 240, x \geq 10, x+y \leq 20 $$ D 120

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The correct system of inequalities is $$ 12x + 16y \geq 8240, x \geq 10, x + y \leq 20 $$. The closest option is D, but with the understanding that the earnings threshold should be $$ 8240 $$.

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