SOLUTION: What quantity of a 40% acid solution must be mixed with a 10% solution to produce 300 quarts of a 30% solution?

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Question 640216: What quantity of a 40% acid solution must be mixed with a 10% solution to produce 300 quarts of a 30% solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of 40% solution needed
Let +b+ = quarts of 10% solution needed
given:
(1) +a+%2B+b+=+300+
(2) +%28+.4a+%2B+.1b+%29+%2F+300+=+.3+
------------------------
(2) +.4a+%2B+.1b+=+.3%2A300+
(2) +.4a+%2B+.1b+=+90+
(2) +4a+%2B+b+=+900+
Subtract (1) from (2)
(2) +4a+%2B+b+=+900+
(1) +-a+-+b+=+-300+
+3a+=+600+
+a+=+200+
and since
(1) +a+%2B+b+=+300+
(1) +b+=+100+
200 quarts of 40% solution is needed
100 quarts of 10% solution is needed
check:
(2) +%28+.4%2A200+%2B+.1%2A100+%29+%2F+300+=+.3+
(2) +%28+80+%2B+10+%29+%2F+300+=+.3+
(2) +90+%2F+300+=+.3+
(2) +90+=+.3%2A300+
(2) +90+=+90+
OK