G1.2 Let $[x]$ be the largest integer not greater than $x$. For example, $[2.5]=2$.
$\begin{array}{l}\text { If } b=\left[100 \times \frac{11 \times 77+12 \times 78+13 \times 79+14 \times 80}{11 \times 76+12 \times 77+13 \times 78+14 \times 79}\right], \text { find the value of } b \text {. } \\ 100 \times \frac{11 \times 77+12 \times 78+13 \times 79+14 \times 80}{11 \times 76+12 \times 77+13 \times 78+14 \times 79} \\ =100 \times \frac{11 \times 76+12 \times 77+13 \times 78+14 \times 79+11+12+13+14}{11 \times 76+12 \times 77+13 \times 78+14 \times 79} \\ =100 \times\left(1+\frac{11+12+13+14}{11 \times 76+12 \times 77+13 \times 78+14 \times 79}\right) \\ =100+\frac{11 \times 100+12 \times 100+13 \times 100+14 \times 100}{11 \times 76+12 \times 77+13 \times 78+14 \times 79} \\ 11 \times 76+12 \times 77+13 \times 78+14 \times 79<11 \times 100+12 \times 100+13 \times 100+14 \times 100<2(11 \times 76+12 \times 77+13 \times 78+14 \times 79) \\ 1<\frac{11 \times 77+12 \times 78+13 \times 79+14 \times 80}{11 \times 76+12 \times 77+13 \times 78+14 \times 79}<2 \\ 101<100 \times \frac{11 \times 77+12 \times 78+13 \times 79+14 \times 80}{11 \times 76+12 \times 77+13 \times 78+14 \times 79}<102, b=101\end{array}$