Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. a sandwich costs $2, and hot lunch costs $3.

this system of inequalities models the scenario:

2x + 3y ≤ 15
x + y ≥ 3

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 (5, 1) 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) see the explanation

Part B) The point (5,1) is included in the solution area for the system

Part C) I choose the point (2,3), that means Michael buys 2 sandwich and 3 hot lunch

Step-by-step explanation:

Part A)

Let

x -----> number of sandwich

y ----> number of hot lunch

we have

----> inequality A

The solution of the inequality A is the shaded area below the solid line

-----> inequality B

The solution of the inequality B is the shaded area above the solid line

Using a graphing tool

The solution of the system of inequalities is the shaded area between the positive integers (whole numbers) of x and y

see the attached figure

Part B) is the point (5,1) included in the solution area for the system? Justify your answer mathematically

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system (the ordered pair is included in the solution area for the system)

Verify Inequality A

For x=5, y=1

substitute

----> is true

so

The ordered pair satisfy inequality A

Verify Inequality B

For x=5, y=1

substitute

----> is true

so

The ordered pair satisfy inequality B

The ordered pair satisfy both inequalities

therefore

The point (5,1) is included in the solution area for the system

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

I choose the point (2,3)

The point (2,3) is included in the solution area for the system

see the attached figure N 2

That means

Michael buys 2 sandwich and 3 hot lunch

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05