SOLUTION: how many liters of a 50% acid solution must be mixed with a 15% acid solution to get a 210L 40% solution I came up with .5x+.15(x-210)=.40(210) but keep getting it wrong

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Question 945961: how many liters of a 50% acid solution must be mixed with a 15% acid solution to get a 210L 40% solution
I came up with .5x+.15(x-210)=.40(210)
but keep getting it wrong

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 50% acid solution needed
+.5a+ = liters of acid in 50% solution
Let +b+ = liters of 15% acid solution needed
+.15b+ = liter od acid is 15% solution
------------------------------------------
(1) +a+%2B+b+=+210+
(2) +%28+.5a+%2B+.15b+%29+%2F+210+=+.4+
--------------------------------
(2) +.5a+%2B+.15b+=+.4%2A210+
(2) +.5a+%2B+.15b+=+84+
(2) +50a+%2B+15b+=+8400+
(2) +10a+%2B+3b+=+1680+
--------------------------
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +10a+%2B+3b+=+1680+
(1) +-3a+-+3b+=+-630+
------------------------
+7a+=+1050+
+a+=+150+
and, since
(1) +a+%2B+b+=+210+
(1) +150+%2B+b+=+210+
(1) +b+=+60+
150 liters of 50% acid solution are needed
60 liters of 15% acid solution are needed
check:
(2) +%28+.5%2A150+%2B+.15%2A60+%29+%2F+210+=+.4+
(2) +%28+75+%2B+9+%29+%2F+210+=+.4+
(2) +84+=+.4%2A210+
(2) +84+=+84+
Ok