Mark and Ann together were allocated n boxes of cookies

BTGModeratorVI wrote: ↑

Fri Mar 06, 2020 5:46 pm

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: A
Source: Official Guide

Mark sold 10 boxes less than n and Ann sold 2 boxes less than n
We can write:
n - 10 = number of boxes that Mark sold
n - 2 = number of boxes that Ann sold

Together they (Mark and Ann) have sold less than n boxes
In other words: (# boxes Mark sold) + (# boxes Ann sold) < n
Rewrite as: (n - 10) + (n - 2) < n
Simplify: 2n - 12 < n
Add 12 to both sides: 2n < n + 12
Subtract n from both sides: n < 12

What is the value of n?
We know that n < 12
Check the answer choices . . . only answer choice A (11) is less than 12

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Fri Mar 06, 2020 5:46 pm

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: A
Source: Official Guide

We are given that Mark and Ann were given n boxes of cookies to sell. Mark sold (n - 10), and Ann sold (n - 2) boxes of cookies; thus, together they sold n - 10 + n - 2 = 2n - 12 boxes of cookies. Since together they sold fewer than n boxes, we can create the following inequality:

2n - 12 < n

n < 12

The only answer that is less than 12 is 11.

Answer: A