Respuesta :
let's say we use "x" of the 25% OJ... ok... well, how much juice is really in that "x" liters? well, 25% of it is OJ, the rest is water, how much is 25% of x? well, (25/100) * x, or 0.25x.
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7[/tex]
how much will be it of the 10% juice? well, y = 15 - x.
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7[/tex]
how much will be it of the 10% juice? well, y = 15 - x.
