Question

One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice

Answer 1

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.

$\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7$

how much will be it of the 10% juice?  well, y = 15 - x.