Answer:
The solution set to the system of inequalities is the shaded region where both conditions, ( x + 5y \leq 15 ) and ( x + y \geq 4 ), are satisfied simultaneously.
Step-by-step explanation:
Part A:
Let's define two variables:
- \( x \) for the number of servings of dry food.
- \( y \) for the number of servings of wet food.
The system of inequalities that models this scenario is:
1. \( x + 5y \leq 15 \) (Michelle cannot spend more than $15)
2. \( x + y \geq 4 \) (She wants to feed at least four dogs)
Part B:
The graph of this system will have two inequalities represented by shaded regions:
1. The inequality \( x + 5y \leq 15 \) will be graphed as a line that starts at \( (15, 0) \) on the x-axis and goes to \( (0, 3) \) on the y-axis. This line will be solid, indicating that points on the line are included in the solution set. The area below and to the left of this line will be shaded, representing all the combinations of \( x \) and \( y \) that do not exceed Michelle's budget.
2. The inequality \( x + y \geq 4 \) will be graphed as a line that starts at \( (4, 0) \) on the x-axis and goes to \( (0, 4) \) on the y-axis. This line will also be solid, and the area above and to the right of this line will be shaded, representing all the combinations of \( x \) and \( y \) that ensure at least four dogs are fed.
The solution set is the area where the shaded regions of both inequalities overlap. This region represents all the possible combinations of dry and wet food servings that Michelle can buy with her $15 to feed at least four dogs. The boundary lines of the solution set will be solid, and the vertices of the solution set will be the points where the lines intersect with each other and the axes. Points within this region (including the boundary lines) are the solutions to the system of inequalities.
Answer:
The correct answer is 54
Step-by-step explanation:
50 + 4 = 54