Answer:
[tex]x\leq 25\\y\geq 10\\.50x + y\geq 30[/tex]
Step-by-step explanation:
It is given that,
Amy wants to sell at most 25 cookies ,
Let number of cookies be '[tex]x[/tex]' , then [tex]x[/tex] should be less than or equal to 25
Which is represented by [tex]x\leq 25[/tex] ,
Further,
Let number of sprites be '[tex]y[/tex]', then '[tex]y[/tex]' should be greater than or equal to 10
Which is represented by [tex]y\geq 10[/tex]
Also,
Given,
she profits $.50 on every cookie
and $1.00 on every sprite.
So total profit on selling cookies would be
= Profit on each cookie times the number of cookies
=[tex].50\times x[/tex]
=[tex].5x[/tex]
Similarly, total profit on selling sprites would be
=profit on each sprite times the number of sprites
=[tex]1.00\times y[/tex]
=[tex]y[/tex]
Now, combining these two should be greater than or equal to $30
representing this through an equation,
[tex].50x+y\geq 30[/tex]
Thus the sysytem of equations is given as:
[tex]x\leq 25\\y\geq 10\\.50x + y\geq 30[/tex]
