SOLUTION: Scott wants to make 6 gal of a 50% sugar solution by mixing together a 60% sugar solution and pure water. How much of each solution must he use?

Algebra ->  Expressions-with-variables -> SOLUTION: Scott wants to make 6 gal of a 50% sugar solution by mixing together a 60% sugar solution and pure water. How much of each solution must he use?       Log On


   

Question 1069883: Scott wants to make 6 gal of a 50% sugar solution by mixing together a 60% sugar solution and pure water. How much of each solution must he use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 60% sugar solution needed
+.6a+ = gallons of sugar in 60% solution
Let +b+ = gallons of water needed
-----------------------------------------------
(1) +a+%2B+b+=+6+
(2) ++.6a++%2F+6+=+.5+
------------------------
(2) +.6a+=+3+
(2) +a+=+5+
and
(1) +a+%2B+b+=+6+
(1) +5+%2B+b+=+6+
(1) +b+=+1+
--------------------
5 gallons of 60% sugar solution is needed
1 gallon of water is needed
---------------------------
check:
(2) ++.6a++%2F+6+=+.5+
(2) ++.6%2A5++%2F+6+=+.5+
(2) +3%2F6+=+.5+
(2) +.5+=+.5+
OK