$3 \cdot 20$ Four children buy a small boat for 60 dollars. The first child pays half of what the other children pay in total, the second child pays one-third of what the other children pay in total, the third child pays one-fourth of what the other children pay in total. The fourth child should pay
(A) 10 dollars.
(B) 12 dollars.
(C) 13 dollars.
(D) 14 dollars.
(E) 15 dollars.
(29th American High School Mathematics Examination, 1978)
[Solution] Let $w, x, y$ and $z$ be the amounts in dollars paid by the first, second, third, and fourth child, respectively. Then we have
$$
w+x+y+z=60,
$$

and $w=\frac{1}{2}(x+y+z)=\frac{1}{2}(60-w)$, which gives $w=20$;
also $x=\frac{1}{3}(w+y+z)=\frac{1}{3}(60-x)$, which gives $x=15$;
and $y=\frac{1}{4}(w+x+z)=\frac{1}{4}(60-y)$, which gives $y=12$;
thus
$$
z=13 \text {. }
$$

Therefore, the answer is $(C)$.