SOLUTION: How many gallons of a 60% salt solution must be mixed with 30 gallons of a 13% solution to obtain a solution that is 50% salt?

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Question 455082: How many gallons of a 60% salt solution must be mixed with 30 gallons of a 13% solution to obtain a solution that is 50% salt?
Found 2 solutions by amoresroy, josmiceli:
Answer by amoresroy(361) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the no. gallons of a 60% salt solution that must be mixed with 30 gallons of a 13% solution to obtain a solution that is 50% salt
.6x + 30(.13) = .5(30 + x)
.6x + 3.9 = 15 + .5x
.1x = 11.1
x = 111
111 gallons of a 60% salt solution that must be mixed with 30 gallons of a 13% solution to obtain a solution that is 50% salt.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 60% solution needed
given:
+.6a+ = gallons of salt in 60% solution
+.13%2A30+=+3.9+ = gallons of salt in 60% solution
+%28.6a+%2B+3.9%29+%2F+%28+a+%2B+30%29+=+.5+
+.6a+%2B+3.9+=+.5%2A%28+a+%2B+30+%29+
+.6a+%2B+3.9+=+.5a+%2B+15+
+.1a+=+11.1+
+a+=+111+
111 gallons of 60% solution are needed
check answer:
+%28.6a+%2B+3.9%29+%2F+%28+a+%2B+30%29+=+.5+
+%28.6%2A111+%2B+3.9%29+%2F+%28+111+%2B+30%29+=+.5+
+%28+66.6+%2B+3.9%29+%2F+141+=+.5+
+70.5+%2F+141+=+.5+
+70.5+=+.5%2A141+
+70.5+=+70.5+
OK