Question

One canned juice drink is 15% orange juice another is 10% orange juice how many liters of each should be mixed together in order to get 5 L that is 14% orange juice

Answer 1

`\bf \begin{array}{lccclll} &quantity(L)&concentration& \begin{array}{llll} concentrated\\ quantity \end{array}\\ &-----&-------&-------\\ \textit{15\% juice}&x&0.15&0.15x\\ \textit{10\% juice}&y&0.10&0.10y\\ -----&-----&-----&-----\\ mixture&5&0.14&(5)(0.14) \end{array}`

whatever the amounts of "x" and "y" are, they must add up to 5Liters
thus x + y = 5

and whatever the concentrated quantity is in each, they must add up to (5)(0.14)

notice, that we use the decimal notation for the amount of juice concentration, that is, 15% is just 15/100 or 0.15, and 14% is just 14/100 or 0.14 and so on, recall that "whatever% of something" is just (whatever/100)*something

thus
`\bf \begin{cases} x+y=5\implies \boxed{y}=5-x\\\\ 0.15x+0.10y=(5)(0.14)\\ ----------\\ 0.15x+0.10\left(\boxed{5-x} \right)=(5)(0.14) \end{cases}`

solve for "x", to see how much of the 15% juice will be needed

what about "y"? well, y = 5 - x