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