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Jack is selling wristbands and headbands to earn money for camp. He earns $2 for each wristband and $3 for each headband. He wants to earn at least $50. He needs to sell at least 5 wristbands. Which system of inequalities is shown in the graph of the solution below?

• 2x + 3y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0
•3x + 2y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0
•2x + 3y ≤ 50 x ≥ 5 x ≥ 0 y ≥ 0
•2x + 3y ≤ 50 x ≤ 5 x ≥ 0 y ≥ 0

Respuesta :

Your answer will most likely be a.

Answer:

The correct option is A.

Step-by-step explanation:

Let number of sold wristbands and headbands be x and y respectively.

It is given that the jack earns $2 for each wristband and $3 for each headband. So, total revenue is

[tex]T=2x+3y[/tex]

He wants to earn at least $50.

[tex]2x+3y\geq 50[/tex]

He needs to sell at least 5 wristbands.

[tex]x\geq 5[/tex]

The number of sold wristbands and headbands can not be negative. so,

[tex]x\geq 0,y\geq 0[/tex]

The system of inequalities is

[tex]2x+3y\geq 50[/tex]

[tex]x\geq 5[/tex]

[tex]x\geq 0,y\geq 0[/tex]

Therefore, correct option is A.

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