Question

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

Answer 1

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