well, let's say we need "g" of grape punch, now how much juice is in the "g" amount? well, just 10% of it is juice or (10/100) * g, 0.1g.
let's say we need "b" of berry punch, now, is 20% juice, how much juice in "b"? well, (20/100) * b, or 0.2b.
whatever "g" and "b" are, they must add up to 12 cups, of 18%, how much juice in 12cups? well (18/100) * 12, or 2.16
[tex]\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-----&-----\\
\textit{grape punch}&g&0.10&0.10g\\
\textit{berry punch}&b&0.20&0.20b\\
-----&-----&-----&-----\\
mixture&12&0.18&2.16
\end{array}[/tex]
[tex]\bf \begin{cases}
g+b=12\implies \boxed{b}=12-g\\
0.1g+0.2b=2.16\\
----------\\
0.1g+0.2\left( \boxed{12-g} \right)=2.16
\end{cases}
\\\\\\
0.1g+2.4-0.2g=2.16\implies 2.4-2.16=0.2g-0.1g
\\\\\\
0.24=0.1g\implies \cfrac{0.24}{0.1}=g\implies \boxed{2.4=g}[/tex]
and of berry will then be 12 - g
