Solution: First, calculate the sum of the expressions: $(3u - 4) + (7u + 2) + (4u - 1) = 14u - 3$. Divide by 3 to find the average: $\frac14u - 33$. Since $u$ is a positive multiple of 3 and $u^2 < 100$, possible values for $u$ are 3, 6. Testing $u = 3$: $\frac14(3) - 33 = \frac42 - 33 = \frac393 = 13$. For $u = 6$, $u^2 = 36 < 100$, but $14(6) - 3 = 81$, $\frac813 = 27$. However, the problem implies a unique answer, so the smallest valid $u = 3$ gives $\boxed13$. - Abu Waleed Tea