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To raise money to attend Boy Scout camp, Alec is selling popcorn. Small bags of popcorn sell for $4 each and large bags sell for $6 each. He needs to earn at least $300 to attend camp. He will also earn a badge if he sells at least 60 bags total of any combination. Write a system of linear inequalities to represent this situation, then graph

Respuesta :

Let's assume

number of small bags of popcorn =x

number of large bags of popcorn =y

He will also earn a badge if he sells at least 60 bags total of any combination

so, we get

[tex]x+y\geq 60[/tex]

Small bags of popcorn sell for $4 each

so, total price of small bags of popcorn =4x

large bags sell for $6 each

so, total price of large bags of popcorn =6x

He needs to earn at least $300 to attend camp

so, we get

[tex]4x+6y\geq 300[/tex]

we know that quantities can never be negative

so, we get

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

so, we get system of inequalities as

[tex]x+y\geq 60[/tex]

[tex]4x+6y\geq 300[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

Graph:


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