Exercise 38 Page 150

Let x represent the number of hours that Louie works as a busboy and y represent the number of hours he works as a clerk.

Knowing that he can work no more than 25, we can say that the sum of the working hours is less than or equal to 25. x+ y ≤ 25 For the inequality that represents the pay, we will make an organized table.

Thus, we have two inequalities to write a system. x+y ≤ 25 & (I) 6.5x+8y≥ 150 & (II) To graph the system, we will start from the first inequality. Let's determine its boundary line. &Inequality I &&Boundary Line I &x+y ≤ 25 &&x+y = 25 The equation of the boundary line is in standard form. In this case, it would be a better way to graph it by finding its intercepts. We will substitute y= 0 for the x-intercept and x= 0 for the y-intercept.

Now we can plot the intercepts and connect them with a line segment. Notice that number of working hours cannot be negative, so it will be bound by the axes. The boundary line will also be solid because of the non-strict inequality.

Next, we should decide which region we will shade. To do so we will test the point (0,0).

Because the point satisfied the inequality, we will shade the region that contains the point. Let's do it!

The second inequality can be graphed by proceeding in the same way. &Inequality II &&Boundary Line II &6.5x+8y ≥ 150 &&6.5x+8y = 150 Next step is to determine the intercepts.

Now that we know the intercepts, we should decide which region we will shade as our final step.

The point did not satisfy the inequality, so we will shade the region that does not contain the point.

The overlapping section is the section that represents the possible combinations.