SOLUTION: how much 2% acid must be mixed with 10% acid to obtain 4000 ml of 4% acid

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Question 782624: how much 2% acid must be mixed with 10% acid to obtain 4000 ml of 4% acid
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 2% acid needed
Let +b+ = ml of 10% acid needed
+.02a+ = ml of acid in 2% acid
+.1b+ = ml of acid in 10% acid
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(1) +a+%2B+b+=+4000+
(2) +%28+.02a+%2B+.1b+%29+%2F+4000+=+.04+
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(2) +.02a+%2B+.1b+=+.04%2A4000+
(2) +.02a+%2B+.1b+=+160+
(2) +2a+%2B+10b+=+16000+
(2) +a+%2B+5b+=+8000+
Subtract (1) from (2)
(2) +a+%2B+5b+=+8000+
(1) +-a+-+b+=+-4000+
+4b+=+4000+
+b+=+1000+
and, since
(1) +a+%2B+b+=+4000+
(1) +a+=+3000+
3000 ml of 2% acid is needed
1000 ml of 10% acid is needed
check:
(2) +%28+.02a+%2B+.1b+%29+%2F+4000+=+.04+
(2) +%28+.02%2A3000+%2B+.1%2A1000+%29+%2F+4000+=+.04+
(2) +%28+60+%2B+100+%29+%2F+4000+=+.04+
(2) +160+=+.04%2A4000+
(2) +160+=+160+
OK