There is a total of 27 quarters stacked in four piles. The first pile has 5 fewer than the second pile. The second pile has 4 more than the third pile. The fourth pile has three times as many as the second pile. How many quarters are in the fourth pile?
Let the number of quarters in the first, second, third, and fourth piles be $a$, $b$, $c$, and $d$, respectively. We have the equations \begin{align*} \tag{1}
a+b+c+d&=27\\ \tag{2}
a&=b-5\\ \tag{3}
b&=c+4\\ \tag{4}
d&=3b
\end{align*} We want to find the value of $d$. We will express each of $a$, $b$, and $c$ in terms of $d$ and then substitute these equations into Equation (1) to find the value of $d$. From Equation (4), we have $b=d/3$. From Equation (3), we have $c=b-4$. Since $b=d/3$, we can rewrite Equation (3) as $c=d/3-4$. We can substitute $b=d/3$ into Equation (2) to get $a=d/3-5$. Substituting $b=d/3$, $c=d/3-4$, and $a=d/3-5$ into Equation (1) to eliminate $a$, $b$, and $c$, we get $(d/3-5)+d/3+(d/3-4)+d=27$, so $d=18$. Thus, there are $\boxed{18}$ quarters in the fourth pile.