SOLUTION: A 25% and a 40% salt solution are combined to make 10 gallons of 35% salt solution. How much of each strength solution is required?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A 25% and a 40% salt solution are combined to make 10 gallons of 35% salt solution. How much of each strength solution is required?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 529855: A 25% and a 40% salt solution are combined to make 10 gallons of 35% salt solution. How much of each strength solution is required?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 25% solution needed
Let b = gallons of 40% solution needed
given:
(1) +a+%2B+b+=+10+
+%28+.25a+%2B+.4b+%29+%2F+10+=+.35+
+.25a+%2B+.4b+=+3.5+
(2) +25a+%2B+40b+=+350+
Multiply both sides of (1) by +25+,
and subtract (1) from (2)
(2) +25a+%2B+40b+=+350+
(1) +-25a+-+25b+=+-250+
+15b+=+100+
+b+=+6.667+
and, since
(1) +a+%2B+b+=+10+
(1) +a+%2B+6.667+=+10+
(1) +b+=+3.333+
3.333 gallons of 25% solution are needed
6.666 gallons of 40% solution are needed
check:
+%28+.25%2A3.333+%2B+.4%2A6.666+%29+%2F+10+=+.35+
+%28.8333+%2B+2.666%29+%2F+10+=+.35+
+3.4999+=+3.5+
close enough
OK