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
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
we know that quantities can never be negative
so, we get
so, we get system of inequalities as
Graph: