Question

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?

A) 11
B) 12
C) 13
D) 14
E) 15

Answer 1

A) 11

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:
`M=n-10`.

Ann sold 2 boxes less than n, so number of boxes of cookies sold by Ann would be
`A=n-2`.

Further we are told that Mark and Ann have each sold at least one box of cookies, so we will get:

`M\geq 1` and
`A\geq 1`.

Now, we can set two inequality as:

`n-10\geq 1` and
`n-2\geq 1`

`n-10+10\geq 1+10` and
`n-2+2\geq 1+2`

`n\geq 11` and
`n\geq 3`

We are also told that together they have sold less than n boxes. We can represent this information in an inequality as:

`n-10+n-2<n`

Let us solve for n.

`2n-12<n`

`2n-12+12<n+12`

`2n-n<n-n+12`

`n<12`

Upon combining our inequalities
`n\geq 11`,
`n\geq 3` and
`n<12`, 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.