One canned juice drink is 20% orange juice, another is 5% orange juice.

How many of each should be mixed in order to get 15 L that is 17% orange juice?

x + y = 15

0.2x + 0.05(15 - y) = 0.17(15)

x ≈ 10.2, y ≈ 4.8

10.2 litres of 20% orange juice and 4.8 litres of 5% orange juice should be

mixed to get 15 litres of 17% orange juice.

Let v be the volume at 5%, so that volume at 20% is 15 - v

15 *17/100 = v/20 + (15 – v)/5, …. multiply by 100

15*17 = 5v + 15*20 – 20v

15v = 15*3, so v = 3 litres and volume at 20% is 12 litres

So of the 15L total mix, 17% is orange juice. That means there is 15 * 0.17 = 2.55 litres of orange juice, with the rest (15 - 2.55 = 12.45) being litres of filler.

let T be the number of litres of the 20% drink, and let F be the number of litres of the 5% drink.

What do we know?

Total volume of liquid = number of litres of 20% + number of litres of 5%

15 = T + F

We can also rewrite this as

15 - T = F

Total litres of just orange juice = (20% of T) + (5% of F)

2.55, as we figured above = 0.2T + 0.05F

But we also just showed that F = 15 - T. So we can substitute that in:

2.55 = 0.2T + 0.05(15 - T)

2.55 = 0.2T + 0.75 - 0.05T

2.55 = 0.15T + 0.75

1.80 = 0.15T

12 = T

And we know F = 15 - T, so F = 3.

CHECK:

total juice contributed by T = 20% * 12 = 2.4L

total juice contributed by F = 5% * 3 = 0.15L

total juice contributed by both = 2.55L, which is 17% of 15 L as we determined

So all terms of the question are met, so we know we're right.

Done!

We indicate with m the number of canned juice at 20% and with n the number of canned juice at 5%.

From the data it follows that:

{m+n=15 ⇒ m=15-n

{0.2*m+0.05*n=0.17*15

We supposed a canned juice is 1L

Plugging the first in the second

0.2(15-n)+0.05n=15*0.17

3-0.2*n+0.05*n=2.55

3-2.55=0.15*n

n=0.45/0.15= 3

hence m=12

Test.

{0.2*12+0.05*3=0.17*15 True, OK!