Mark and ann together were allocated n boxes of cookies to sell for a club project. mark sold 10 boxes less than n and ann sold 2 boxes less than n. if mark and ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n ?

Answer:A) 11Step-by-step explanation:Let M and A represent number of boxes of cookies sold by Mark and Ann respectively.We have been given that Mark sold 10 boxes less than n. We can represent this information as: [tex]M=n-10[/tex].Ann sold 2 boxes less than n, so number of boxes of cookies sold by Ann would be [tex]A=n-2[/tex].Further we are told that Mark and Ann have each sold at least one box of cookies, so we will get:[tex]M\geq 1[/tex] and [tex]A\geq 1[/tex].Now, we can set two inequality as:[tex]n-10\geq 1[/tex]  and  [tex]n-2\geq 1[/tex][tex]n-10+10\geq 1+10[/tex]    and   [tex]n-2+2\geq 1+2[/tex][tex]n\geq 11[/tex]  and [tex]n\geq 3[/tex]We are also told that together they have sold less than n boxes. We can represent this information in an inequality as:[tex]n-10+n-2<n[/tex]Let us solve for n.[tex]2n-12<n[/tex][tex]2n-12+12<n+12[/tex][tex]2n-n<n-n+12[/tex][tex]n<12[/tex]Upon combining our inequalities [tex]n\geq 11[/tex], [tex]n\geq 3[/tex] and [tex]n<12[/tex], we can see that the value of n that will be less than 12 and greater than or equal to 11 is 11. Therefore, the value of n is 11 and option A is correct choice.