G3.1 Let $[x]$ be the largest integer not greater than $x$.
If $A=\left[\frac{2008 \times 80+2009 \times 130+2010 \times 180}{2008 \times 15+2009 \times 25+2010 \times 35}\right]$, find the value of $A$.
Reference: 2008 FGS. 4 Calculate the value of $\frac{2008^{3}+4015^{3}}{2007^{3}+4015^{3}}$.
Let $a=2009, b=130, c=25$
$$
\begin{aligned}
\frac{2008 \times 80+2009 \times 130+2010 \times 180}{2008 \times 15+2009 \times 25+2010 \times 35} & =\frac{(a-1)(b-50)+a b+(a+1)(b+50)}{(a-1)(c-10)+a c+(a+1)(c+10)} \\
& =\frac{a b-b-50 a+50+a b+a b+b+50 a+50}{a c-c-10 a+10+a c+a c+c+10 a+10} \\
& =\frac{3 a b+100}{3 a c+20}=\frac{3 \cdot 2009 \cdot 130+100}{3 \cdot 2009 \cdot 25+20}=\frac{783610}{150695}=5+d
\end{aligned}
$$
where $0<d<1 ; A=5$