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Let $p$ be the number of hours Neyma works per week as a painter and $w$ the number of hours she works per week as a waitress. Since Neyma makes $$20$ per hour working as a painter and $$8$ per hour in the second job, she will earn $20p+8w $ per week. Since she needs to earn at least $$110,$ this expression has to be greater than or equal to $110.$ $20p+8w≥110 $ We also know that Neyma doesn't want to work more than $30$ hours per week, so we can write the second inequality. $p+w≤30 $ The system of inequalities is then ${20p+8w≥110p+w≤30. $

b

${20p+8w≥110p+w≤30 (I)(II) $

${p≥5.5−0.4wp≤30−w $

Now we have to determine if the solution sets lie above or below the lines. The first inequality is $p≥5.5−0.4w $ and describes all $p$-coordinates larger than or equal to $5.5−0.4w$. This means that we have to shade the area above the solid blue line.

The graph of the second inequality

$p≤30−w $ shows a solid green line with shading below it.

The solution to this system of inequalities is area where the shadings overlap. We distinguish this area in the graph below.

c

To name two possible solution, we need any two points from the overlapping area. We will plot the points in the graph and name them.

Two possible solutions are $(10,10)$ and $(6,14).$