Sarah has $8 and wants to buy a combination of cupcakes and fudge to feed at least four siblings. Each cupcake costs $2, and each piece of fudge costs $1. This system of inequalities models the scenario:

2x + y ≤ 8
x + y ≥ 4

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)

Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Part A:

The graph of the system of inequalities consist of two solid lines graphs with the area between the two lines and the y-axis being shaded

The solution set includes, consists of coordinate values that are within the tringle with vertices, (0, 4), (0, 8), (4, 0)

Part B: The point (8, 10), represents, x = 8, and y = 10

Graphically, the point (8, 10) is not included in the solution area

Comparing with the given inequalities, we have;

y ≤ 8 - 2·x

When x = 8, y ≤ 8 - 2 × 8

∴ y ≤ -8

∴ The point (8, 10) is not included in the solution area of the system

Part C: The point (0, 8), which is part of the solution set, which can be represented as y ≤ 8 - 2×0, gives that Sarah buys 8 fudges for $8 to feed less than or equal to 8 siblings but more than or equal to four siblings

Step-by-step explanation:

The given system of inequalities are;

2·x + y ≤ 8

x + y ≥ 4

Where;

x represents the number of cupcakes, and y represents the number of fudges Sara buys

Making y the subject of the inequalities gives;

y ≤ 8 - 2·x

y ≥ 4 - x

Representing the above inequalities in graphical form using Microsoft Excel gives the attached graph with the shaded area showing the feasible region shaded.

it would be 6xy and -16xy.

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