The profit on the sale of a small bag of popcorn is $1, while the profit on the sale of a medium bag of popcorn is $2. The Glee Club expects to sell fewer than 100 total bags of popcorn, but they hope to make more than $100 in profit. The system that represents this is s + m100.

Let number of small bags = s

Let number of medium bags = m

Given profit on 1 small bag = $1

then profit on s bags = 1s

Given profit on 1 medium bag = $2

then profit on m bags = 2m

Now total profit from both type of bags is 1x+2y

profit should be more than $100 so we get inequality

1s+2m>100

Total number of bags are fewer than 100 so we get

s+m<100

which are same as inequalities you found.

Hence your answer is correct.