Question

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.

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

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

Answer 1

The inequality is given by x + y ≥ 3 and 2x + 3y ≤ 15

What is an inequality?

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let y represent the number of sandwich and x represent the number of hot lunch.

Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates, hence:

x + y ≥ 3

Also:

2x + 3y ≤ 15

The inequality is given by x + y ≥ 3 and 2x + 3y ≤ 15

The part of the graph that is darkest is the solution. The point (5, 1) lies on the dark region, hence it is a solution.

Michael can buy 5 sandwich and 1 hot lunch for his classmates.

Find out more on inequality at: https://brainly.com/question/24372553

Answer 2

Answer:

Step-by-step explanation:

A-the first equation which is  2x + 3y ≤ 15 is shaded downwards while the other equation x + y ≥ 3 is shaded upwards

B-(5,1) is included in the solution area for the 2x+3y<15  equation because when x and y are substituted ,it is still less than 15 

so 5+1 is greater than 3

C-(2,3) MICHEAL can buy 2 sandwiches and 3 hot lunches which is Whitin his 15 dollar budget and can feed at least 3 of his classmates ]

i hope this is correct I'm not sure 100% especially part c if it incorrect put comment with correction