You work as a cashier for a bookstore and six dollars per hour

Question

asked May 13, 2023 141k views

1 Answer

Lamia · Answer 1 · 2023-05-16T20:47:53+0000

The phrase " no more than " means in inequality

$\leq$

The phrase " at least" means in inequality

$\ge$

Since she earns $6 per hour for each job, then

Let the number of hours for the first job is x and the number of the hours for the second job is y,

Since she needs to earn at least $60, then the first inequality should be

$6x+6y\ge60$

Divide each term by 6

$\begin{gathered} (6x)/(6)+(6y)/(6)\ge(60)/(6) \\ \\ x+y\ge10 \end{gathered}$

Subtract x from both sides

$\begin{gathered} x-x+y\ge-x+10 \\ y\ge-x+10\rightarrow(1) \end{gathered}$

Since she wants to work no more than 12 hours, then the second inequality should be

$x+y\leq12$

Subtract x from both sides

$\begin{gathered} x-x+y\leq-x+12 \\ y\leq-x+12\rightarrow(2) \end{gathered}$

The correct system is

$\begin{gathered} y\leq-x+12 \\ y\ge-x+10 \end{gathered}$

The answer is A