System of inequalities representing given scenario is as follows
x + y ≤40
5x + 4y ≥ 120
<h3><u>Solution:</u></h3>
Given that Sara sells homemade blueberry jelly (b) and strawberry jam (s) at the farmer's market. She has enough berries for no more than 40 jars.
The blueberry jelly sells for $5 per jar,
And the strawberry jam sells for $4 per jar.
Sara's goal is to make at least $120
Need to write system of inequalities for above scenario.
Let’s assume number of jars of blueberry jelly be represented by variable “x”
And assume number of jars of strawberry jam be represented by variable “y”
<em><u>Let’s create first inequality </u></em>
As it is given that Sara has enough berries for no more than 40 jars, so total number of jars cannot be more than 40.
=> Number jars of blueberry jelly + number of jars of strawberry jam ≤40
=> x + y ≤ 40 ------(1)
<em><u>Now let’s create second inequality
</u></em>
Selling Price of 1 blueberry jelly = $5
So Selling Price of "x" blueberry jelly 
Selling Price of 1 strawberry jam = $4
So Selling Price of "y" strawberry jam = 
So amount generated by selling x blueberry jelly and y strawberry jam = 5x + 4y
And as Sara’s goal is to generate at least $120, so amount generated by selling “x” blueberry jelly and “y” strawberry jam must be greater than $120
=> 5x + 4y ≥ 120 ------ (2)
Hence system of inequalities representing given scenario is as follows
:
x + y ≤40
5x + 4y ≥ 120
will have the most elements when the sets 
and 
are disjoint, i.e. 
, which would mean the most we can can in this case would be
denotes the cardinality of the set