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?

Question

Rylee Benitez

Mathematics

9 May, 21:09

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?

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Answers (1)

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Paulina Booker · Answer 1

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).