Question

You work as a cashier for a grocery store and earn $6 per hour. You also mow lawns and earn $3 per hour. You want to earn at least $30 per week, but you would like to work no more than 12 hours per week.

Given the graph of the linear system, which system is the solution of the real-world problem?

Answer 1

While working as a cashier is x hours. While working as a mow lawns is y hours. So the following system of inequalities is obtained.

$\begin{cases} 3x+6y≥30\\ x+y≤12 \end{cases}$ $\begin{cases} x+2y≥10\\ x+y≤12 \end{cases}$ $\begin{cases} x+2y≥10\\ x≤12-y \end{cases}$ (for example, working on a lawn mower for 10 hours and less than 12 or a cashier for 5 hours and less than 12 you can earn at least 30 dollars).