[tex]\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentration\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{10\% alloy}&x&0.1&0.1x\\
\textit{20\% alloy}&y&0.2&0.2y\\
-----&-----&-------&-------\\
mixture&100&0.17&17
\end{array}[/tex]
now, notice, we use the decimal format for the percent, namely 17% is 17/100 or 0.17 and so on
so.... we know, whatever "x" and "y" is, they must add up to 100 grams
thus x + y = 100
and whatever the concentrated amount is, it must add up to 17 grams for the composition
thus 0.1x + 0.2y = 17
[tex]\bf \begin{cases}
x+y=100\implies \boxed{y}=100-x\\
0.1x+0.2y=17\\
----------\\
0.1x+0.2\left( \boxed{100-x} \right)=17
\end{cases}[/tex]
solve for "x", to see how much is needed of the 10% alloy
what about "y"? well, y = 100 - x
