Question

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)

Answer 1

Sarah can buy 2 cup cakes and 2 fudge for her siblings.

Let x represent the cost of each cupcake and y represent the cost of each fudge.

Since Sarah has $8 to spend, hence:

2x + y ≤ 8  (1)

Also, there are at least four siblings, hence:

x + y ≥ 4    (2)

Plotting equations 1 and 2 using geogebra online tool, the solution is at:

The point (2,2) is a solution.

This means that Sarah can buy 2 cup cakes and 2 fudge for her siblings.

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