Question

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

gether they hope to raise at least $500. The pep club is holding a raffle that will raise at least $100.
The system of inequalities representing this situation is

x+y>500
x>100

both signs have the line thingy under



PLEASEEE HELPPPP AND PLEASE EXPLAIN I DONT UNDERSTAND

Answer 1

Part a) The graph in the attached figure

Part b) see the explanation

Part c) see the explanation

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