Question 962703: A chemist wants to mix three different solutions to create 100 milliliters of a solution that is 13.5% alcohol.Solution A is 10% alcohol, solution B is 15% alcohol and solution C is 30% alcohol. The amount of solution A that is used must be twice the amount of solution B that is used.How many milliliters of each solution should be the chemist combine?
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Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let a = amt of 10%
let b = amt of 15%
let c = amt of 30%
:
A chemist wants to mix three different solutions to create 100 milliliters of a solution that is 13.5% alcohol.
Solution A is 10% alcohol,
solution B is 15% alcohol and
solution C is 30% alcohol.
The amount of solution A that is used must be twice the amount of solution B that is used.
a = 2b
a + b + c = 100
replace a with 2b
2b + b + c = 100
3b + c = 100
then
c = (-3b+100)
the mixture equation
.10a + .15b + .30c = .135(100)
replace a with 2b, replace c with (-3b+100)
.10(2b) + .15b + .30(-3b+100) = 13.5
.20b + .15b - .90b + 30 = 13.5
-.55b = 13.5 - 30
-.55b = -16.5
b = -16.5/-.55
b = + 30 ml of 15% solution
then
2(30) = 60 ml of 10% solution
and
100-30-60 = 10 ml of 30% solution
:
:
Confirm this, see if:
.10(60) + .15(30) + .30(10) = .135(100)
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