1. A system of inequalities that can be written to solve the problem is as follows:
5x + 2.5y ≤ 60
x + y ≥ 14
x ≥ 0, y ≥ 0
2. One possible solution within the shaded region could be x = 8 and y = 6.
We set up a system of inequalities to represent the constraints and then graph them to find a possible solution.
Let's start by defining our variables and setting up the inequalities.
Let x represent the number of hamburgers purchased and y represent the number of tacos purchased.
The constraints are:
Yaritza has 60 to spend, so the total cost of the hamburgers and tacos cannot exceed 60:
1) 5x + 2.50y ≤ 60
Yaritza must buy at least 14 hamburgers and tacos altogether:
2) x + y ≥ 14
Yaritza must buy at least 0 of each item:
3) x ≥ 0, y ≥ 0
We can graph these inequalities to find a possible solution.
Graph the line 5x + 2.50y = 60 by finding the intercepts:
When x = 0, 2.50y = 60, so y = 24
When y = 0, 5x = 60, so x = 12
We plot these points and draw the line.
Next, graph the line x + y = 14 and find the intercepts:
When x = 0, y = 14
When y = 0, x = 14
We plot these points and draw the line.
Finally, shade the region that satisfies all the inequalities.
Thus, one possible solution within this region could be, for example, x = 8 and y = 6, which satisfies all the constraints.