Question

The pep club and honor society are joining forces to raise money for school improvements.

Answer 1

Answer:

Part a) The graph in the attached figure

Part b) see the explanation

Part c) see the explanation

Step-by-step explanation:

Let

x ----> represent pep club donations

y ---> represent donations raised by the honor society

we have

$x+y\geq 500$ ----> inequality A

The solution of the inequality A is the shaded area above the solid line $x+y=500$

$x\geq 100$ ----> inequality B

The solution of the inequality B is the shaded area at right of the solid line $x=100$

Part a) Graph the system of inequalities

using a graphing tool

The solution of the system of inequalities is the shaded area

Remember that the variables x and y cannot be a negative number

see the attached figure

Part b) What does the point (300,100) represent? Is it a viable solution?

The point (300,100) means that the donations raised for pep club  was $300 and the donations raised by the honor society was $100

The point  (300,100) is not a viable solution, because the point not belong to the shaded area of the solution of the system of inequalities

Verify

If the ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequality  

For x=300, y=100  

Inequality A

$300+100\geq 500$      

$400\geq 500$  ----> is not true

The ordered pair not satisfy the inequality A

therefore

The point (300,100) is not a viable solution  

Part c) What does the point (500,200) represent? Is it a viable solution?

The point (500,200) means that the donations raised for pep club  was $500 and the donations raised by the honor society was $200

The point  (500,200) is a viable solution, because the point belong to the shaded area of the solution of the system of inequalities

Verify

If the ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequality  

For x=500, y=200  

Inequality A

$500+200\geq 500$      

$700\geq 500$  ----> is true

The ordered pair satisfy the inequality A

Inequality B

$500\geq 100$ ---> is true

The ordered pair satisfy the inequality B

therefore

The point (500,200) is a viable solution