91Ó°ÊÓ

Consider the given question,

Assume $x$to be the number of liters of $90\%$solution and $y$to be the number of liters of $75\%$solution.

Consider the given question,

$x+y=360......\left(i\right)$

Also, role="math" localid="1644644867399" $90\%of\left(x\right)+75\%of\left(y\right)=85\%of\left(360\right)$

Then,

role="math" localid="1644645068639" $$\begin{gathered} 0.90x+0.75y=0.85\left(360\right) \\ 0.90x+0.75y=306......\left(ii\right) \end{gathered}$$

From equation (i),

role="math" localid="1644645078331" $$\begin{gathered} x+y=360 \\ x=360-y......\left(iii\right) \end{gathered}$$

Substitute the values of $x$in equation (ii),

$$\begin{gathered} 0.9\left(360-y\right)+0.75y=306 \\ 324-0.9y+0.75y=306 \\ -0.15y=-18 \\ y=\frac{-18}{-0.15} \\ y=120 \end{gathered}$$

Substitute the value of $y$in equation (iii),

$$\begin{gathered} x+120=360 \\ x=240 \end{gathered}$$

Substitute the values in equation (i),

$$\begin{gathered} 240+120=360 \\ 360=360 \end{gathered}$$

This is true.

Substitute the values in equation (ii),

$$\begin{gathered} 0.9\left(240\right)+0.75\left(120\right)=306 \\ 216+90=306 \\ 306=306 \end{gathered}$$

This is also true.

Therefore, the number of liters of $90\%$solution is about $240$liters and the number of liters of $75\%$solution is about $120$liters.