Question

PLEASE HELP!!!

Nivyana and Ana are selling their apparel to earn money for a cruise. Knitted scarves are $50, and mittens are $25 per pair. They cannot make more than 30 scarves and mittens combined. They need to earn at least $1000 to pay for the cruise and souvenirs.


Part A:Write the inequalities that would represent the situation

Part B: GRAPH the system of linear inequalities and shade where the solutions are.

Part C: Identify two possible solutions to Nivyana and Ana's situation

--------- scarves ------------scarves

---------------mittens -----------mittens

Answer 1

Explanation:

Part A:

Let
`m` be the number of mittens and
`s` be the number of scarves. Then we have the inequalities:

`s+m\leq 30.` This says Nivyana and Ana cannot make more than 30 scarves

`50s+25m\geq 1000.` This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)