Answer:
A) 11
Step-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.
