SOLUTION: Theresa Yee, a chemist, has 25% hydrochloric acid solution and a 50% hydrochloric acid solution. How many liters of each should she mix to get 10 liters of a hydrochloric acid solu

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Question 451165: Theresa Yee, a chemist, has 25% hydrochloric acid solution and a 50% hydrochloric acid solution. How many liters of each should she mix to get 10 liters of a hydrochloric acid solution with a 40% acid concentration?
Found 2 solutions by rwm, josmiceli:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
.25x+.5y=.4*10
x+y=10
x=4 y=6

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of 25% solution needed
Let b = liters of 50% solution needed
given:
(1) +a+%2B+b+=+10+ liters
(2) +%28.25a+%2B+.5b%29+%2F+10+=+.4+
--------------------
(2) +.25a+%2B+.5b+=+4+
(2) +25a+%2B+50b+=+400+
Multiply both sides of (1) by 25 and
subtract (1) from (2)
(2) +25a+%2B+50b+=+400+
(1) +-25a+-+25b+=+-250+
+25b+=+150+
+b+=+6+
and, since
(1) +a+%2B+b+=+10+
+a+=+4+
4 liters of 25% solution are needed
6 liters of 50% solution are needed
check:
(2) +%28.25a+%2B+.5b%29+%2F+10+=+.4+
(2) +%28.25%2A4+%2B+.5%2A6%29+%2F+10+=+.4+
(2) +%281+%2B+3%29%2F10+=+.4+
(2) +4%2F10+=+.4+
OK