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?

X=amount of canned juice with 25% of orange juice
y=amount of other canned juice with 10% of orange juice.
25%=25/100=1/4
10%=10/100=1/10
17%=17/100
We can suggest this system of equations:
(1)    x+y=15

(2)    (x/4+y/10) / (x+y)=17/100  ⇒100(x/4 + y/10)=17(x+y)  ⇒25x+10y=17x+17y  ⇒8x-7y=0

Finally, we have this system of equations:
x+y=15
8x-7y=0

We can solve this system by substitution method. 
x+y=15      ⇒    y=15-x

8x-7(15-x)=0
8x-105+7x=0
15x=105
x=105/15
x=7

y=15-x=15-7=8

we should mix 7 liters of juice (with 25% orange juice) and 8 liters of juice (with 10% orange juice).