SOLUTION: this is a word problem i cant figure it out please help: one canned juice drink is 20% orange juice, another os 10% orange juice. How many liters pf each should be mixed togethre i

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Question 220821: this is a word problem i cant figure it out please help: one canned juice drink is 20% orange juice, another os 10% orange juice. How many liters pf each should be mixed togethre in order to get 10L that is 12% orange juice?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of 20% juice needed
Let b = liters of 10% juice needed
given:
(1) a+%2B+b+=+10 liters of 12% mixture
OJ in 20% juice is .2a liters
OJ in 10% juice is .1b liters
OJ in 12% juice is .12%2A10+=+1.2 liters
In words:
(liters OJ in 20% mix + liters OJ in 10% mix)/(total liters of 12% mix) = 12%
%28.2a+%2B+.1b%29%2F10+=+.12
.2a+%2B+.1b+=+1.2
(2) 2a+%2B+b+=+12
Subtract (1) from (2)
(2) 2a+%2B+b+=+12
(1) -a+-+b+=+-10
a+=+2 liters
and, since
a+%2B+b+=+10
2+%2B+b+=+10
b+=+8 liters
2 liters of the 20% juice and 8 liters of the 10%
juice need to be mixed
check answer:
%28.2a+%2B+.1b%29%2F10+=+.12
%28.2%2A2+%2B+.1%2A8%29%2F10+=+.12
%28.4+%2B+.8%29%2F10+=+.12
1.2%2F10+=+.12
1.2+=+1.2
OK