SOLUTION: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 40% salt and Solution B is 65% salt. She wan

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Question 911579: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
40%
salt and Solution B is
65%
salt. She wants to obtain
100
ounces of a mixture that is
50%
salt. How many ounces of each solution should she use?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of A needed
Let +b+ = ounces of B needed
---------------
+.4a+ = ounces of salt in A
+.65b+ = ounces of salt in B
---------------------------
(1) +a+%2B+b+=+100+
(2) +%28+.4a+%2B+.65b+%29+%2F+100+=+.5+
-----------------------------
(2) +.4a+%2B+.65b+=+50+
Multiply both sides by +100+
(2) +40a+%2B+65b+=+5000+
Multiply both sides of (1) by +40+
and subtract (1) from (2)
--------------------------------
(2) +40a+%2B+65b+=+5000+
(1) +-40a+-+40b+=+-4000+
--------------------------
+25b+=+1000+
+b+=+40+
and, since
(1) +a+%2B+b+=+100+
(1) +a+=+60+
------------------
60 ounces of A is needed
40 ounces of B is needed
-------------------------
check:
(2) +%28+.4a+%2B+.65b+%29+%2F+100+=+.5+
(2) +%28+.4%2A60+%2B+.65%2A40+%29+%2F+100+=+.5+
(2) +%28+24+%2B+26+%29+%2F+100+=+.5+
(2) +50+=+.5%2A100+
(2) +50+=+50+
'OK