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?

Question

William Hartman

Mathematics

13 November, 13:58

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?

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Answers (1)

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Paityn Carney · Answer 1

n = 11.

Explanation:

Let m be the number of boxes Mark sells and a be the number of boxes Ann sells.

Since Mark sells 10 less than n, m = n-10. Since Ann sells 2 less than n, a = n-2.

Together, they sold n-10+n-2=2n-12 boxes.

We know that they sold less than n boxes, so our inequality would be

2n-12
To solve this, subtract n from both sides:

2n-12-n
Add 12 to both sides:

n-12+12<0+12; n<12.

This means there were less than 12 boxes. The next number down is 11; this woks because Mark sold 10 less than n; 11-10=1. Mark sold at least 1 box.

If n=10, however, 10-10=0; this doesn't work, because Mark did sell at least 1 box.