LakerFan24 wrote:
Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?
A) \(\frac{(n+m)}{2n}\)
B) \(\frac{(m-n)}{2}\)
C) \(\frac{(n-m)}{2}\)
D) \(\frac{(m+n)}{2}\)
E) \(\frac{(n}{2+m)}\)
Hi...
I. Logically..
Since Missy ate more than Audrey and both finished n crackers..
Missy has to eat MORE than half that is >\(\frac{n}{2}\)..
Only D is left..
II. Substitution..
Take total as 10 and M ate 6 and A ate 4...
So m =6-4=2 and n=10..
Substitute in choices and see which gives answer as 6..
A) \(\frac{(n+m)}{2n}....=\frac{10+2}{2*10}\)..No
B) \(\frac{(m-n)}{2}...=\frac{2-10}{2}\)..no
C) \(\frac{(n-m)}{2}...=\frac{10-2}{4}\)..no
D) \(\frac{(m+n)}{2}=\frac{10+2}{2}\).. Yes
E) \(\frac{(n}{2+m)}=10/2+2\)..No
D
III. Algebra..
Let Missy eat x and Audrey eat y..
x-y=m and x+y=n....
Since we are looking for X, add two equations..
So x-y+x+y=m+n......2x=m+n.......x=(m+n)/2
D
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