We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]
Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]
as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]
Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]
THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]
