SOLUTION: a chemist is going to mix a 15% acid solution with a 45% acid solutionm how many liters of each solution should she mix in order to get 48 liters of a 20% acid solution?

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Question 305402: a chemist is going to mix a 15% acid solution with a 45% acid solutionm how many liters of each solution should she mix in order to get 48 liters of a 20% acid solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
She ends up with .2%2A48+=+9.6 liters of acid in
48 liters of solution
Let a = liters of 15% solution to use
Let b = liters of 45% solution to use
(1) %28.15a+%2B+.45b%29%2F48+=+.2
(1) .15a+%2B+.45b+=+9.6
(1) 15a+%2B+45b+=+960
and
(2) a+%2B+b+=+48
Multiply both sides of (2) by 15 and
subtract (2) from (1)
---------------------
(1) 15a+%2B+45b+=+960
(2) -15a+-+15b+=+-720
30b+=+240
b+=+8
and
a+%2B+8+=+48
a+=+40
She must mix 40 liters of the 15% solution
with 8 liters of the 45% solution
check answer:
(1) %28.15a+%2B+.45b%29%2F48+=+.2
(1) %28.15%2A40+%2B+.45%2A8%29%2F48+=+.2
%286+%2B+3.6%29%2F48+=+.2
9.6%2F48+=+.2
9.6+=+9.6
OK