SOLUTION: please solve a solution containing 30% juice is mixed with a solution containing 10% juice to make 100 gallons of solution that makes 12% juice.How much of the 30% solution wa

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Question 267345: please solve

a solution containing 30% juice is mixed with a solution containing 10% juice to make 100 gallons of solution that makes 12% juice.How much of the 30% solution was used?

Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
.30x+.10(100-x)=.12*100
.30x+10-.10x=12
.20x=12-10
.20x=2
x=2/.2
x=10 gallons of 30% solution is used.
100-10=90 gallons 0f 10% is used.
Proof:
.30*10+.10*90=.12*100
3+9=12
12=12

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(gallons of juice in 1st solution + gallons of juice in 2nd solution / (gallons of final solution) = 12%
Let a = gallons of 30% solution needed
Let b = gallons of 10% solution needed
given:
(1) a+%2B+b+=+100
------------------
%28.3a+%2B+.1b%29%2F100+=+.12
.3a+%2B+.1b+=+12
(2) 3a+%2B+b+=+120
Now subtract (1) from (2)
(2) 3a+%2B+b+=+120
(1) -a+-+b+=+-100
2a+=+20
a+=+10
and, since
a+%2B+b+=+100
b+=+100+-+10
b+=+90
10 gallons of the 30% solution were needed
check:
%28.3a+%2B+.1b%29%2F100+=+.12
%28.3%2A10+%2B+.1%2A90%29%2F100+=+.12
%283+%2B+9%29%2F100+=+.12
12%2F100+=+.12
.12+=+.12
OK