  There exists a minimum integer $N$ such that any 2-coloring of
$\{1,2,...,N\}$ admits a monochromatic solution to $x+y+kz =\ell w$ for $k,\ell
\in \mathbb{Z}^+$, where $N$ depends on $k$ and $\ell$. We determine $N$ when
$\ell-k \in \{0,1,2,3,4,5\}$, for all $k,\ell$ for which
${1/2}((\ell-k)^2-2)(\ell-k+1)\leq k \leq \ell-4$, as well as for arbitrary $k$
when $\ell=2$.
