SOLUTION: i need help with this. A 45% salt solution was mixed with a 75% salt solution to produce 15 kilograms of solution that was 67% salt. how much of each solution was used?

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Question 705073: i need help with this. A 45% salt solution was mixed with a 75% salt solution to produce 15 kilograms of solution that was 67% salt. how much of each solution was used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kg of 45% salt solution needed
Let +b+ = kg of 75% salt solution needed
given:
(1) +a+%2B+b+=+15+
(2) +%28+.45a+%2B+.75b+%29+%2F+15+=+.67+
-----------------------------
(2) +.45a+%2B+.75b+=+.67%2A15+
(2) +.45a+%2B+.75b+=+10.05+
(2) +45a+%2B+75b+=+1005+
Multiply both sides of (1) by +45+
and subtract (1) from (2)
(2) +45a+%2B+75b+=+1005+
(1) +-45a+-+45b+=+-675+
+30b+=+330+
+b+=+11+
and,, since
(1) +a+%2B+b+=+15+
(1) +a+%2B+11+=+15+
(1) +a+=+4+
4 kg of 45% salt solution is needed
11 kg of 75% salt solution is needed
check:
(2) +%28+.45a+%2B+.75b+%29+%2F+15+=+.67+
(2) +%28+.45%2A4+%2B+.75%2A11+%29+%2F+15+=+.67+
(2) +%28+1.8+%2B+8.25+%29+%2F+15+=+.67+
(2) +10.05+%2F+15+=+.67+
(2) +10.05+=+.67%2A15+
(2) +10.05+=+10.05+
OK