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

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Answer 1 · 2016-12-18T02:39:33

#9# liters of 15% orange juice and #1# liter of 5 % orange juice.

Let #x# be the number of liters of #15%# juice, and
#y# be the number of liters of #5%# juice.

Then #x + y = 10#

and #0.15x + 0.05y = 1.4#

(there are #1.4# liters of orange juice in a 14% solution of 10 liters--made up of #0.15x# liters of #15%#, and #0.05y# of #5%#)

These equations can be easily solved.

Divide the second by #.05" "rarr: 3x + y = 28#
Then subtract the first equation:

#(3x + y) - (x + y) = 28 - 10#
#3x +y -x -y = 18#

which simplifies to # 2x = 18#

So #x =9#

And since #x + y = 10#, we get #y = 1#