Newtons Law conceptual question

1. The problem statement, all variables and given/known data

Two boxes of masses m and 3m are stacked.
The surface between the more massive box and
the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide
on the more massive box, what is t
he static friction force on the less massive box?
A) F
B) F/2
C) F/3
D) F/4

The answer is D.

2. Relevant equations
∑F=F=Ma
Ff=m(F3m)

So F= (F/3)

3. The attempt at a solution

∑Flarge=F=Ma
Ff=m(F3m)
∑Fsmall=Ff=ma
So F= (F/3)

I keep getting C as the answer. However, the solutions manual claims that the answer is D (I also asked my professor and he too said it is) Can anyone explain to me why it is D? Thank you.

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