first off, let's convert the percentages to decimal format, so our 77% turns to 77/100 or 0.77, and our 55% turns to 55/100 or 0.55 and so on
now, the sum of both salines, must add up to the 77% mixture, let's say is "y"
so, 11 + 4 = y, and whatever the concentration level is, must also sum up to the mixture's concentration of 77%
anyway thus
[tex]\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{first sol'n}&11&x&11x\\
\textit{second sol'n}&4&0.55&2.20\\
------&-----&-------&-------\\
mixture&y&0.77&0.77y
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
11+4=y\implies 15=\boxed{y}\\
11x+2.2=0.77y\\
----------\\
11x+2.2=0.77\cdot \boxed{15}
\end{cases}[/tex]
solve for "x"
