10. On the label with the list of ingredients of a confectionery product, it can be read: sugar, cocoa, hazelnuts $16 \%$, palm oil, milk $4 \%$. Knowing that the ingredients are listed in order (no ingredient can be present in a higher quantity than another listed before it), what is the maximum percentage of cocoa that the confectionery could contain?
(A) $22 \%$
(B) $21 \%$
(C) $40 \%$
(D) $38 \%$
(E) $80 \%$
Problem 10. The answer is (D).

Let's call $z, c, p$ the quantities of sugar, cocoa, and palm oil present in the product (expressed as a percentage). We know that $z+c+p=80$, and that $4 \leq p \leq 16 \leq c \leq z$. The maximum percentage of cocoa that the product could contain is obtained for the minimum values of the other two ingredients, compatible with these equations and inequalities; that is, for $p=4$ and $z=c$. Therefore, $c=(80-4) / 2=38$.

(Problem proposed by F. Poloni)