SOLUTION: solve using a system of equations. I know you have to do something like x+y+x+y=, but then I get so confused. A 40% saline solution is to be mixed with a 60% saline solution

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Question 408464: solve using a system of equations.
I know you have to do something like x+y+x+y=, but then I get so confused.
A 40% saline solution is to be mixed with a 60% saline solution to obtain 8 liters of a 55% solution. How many liters of each solution should be used?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(liters of salt in 40% solution + liters of salt in 60% solution)/(liters of solution) = 55%
Let a = liters of 40% solution needed
Let b = liters of 60% solution needed
---------------------------------
given:
.4a = salt in 40% solution
.6b = salt in 60% solution
------------------------
(1) %28.4a+%2B+.6b%29%2F8+=+.55
(2) a+%2B+b+=+8
This is 2 equations and 2 unknowns, so it's solvable
----------------------
(1) %28.4a+%2B+.6b%29%2F8+=+.55
(1) .4a+%2B+.6b+=+.55%2A8
(1) .4a+%2B+.6b+=+4.4
(1) 40a+%2B+60b+=+440
and, also,
(2) a+%2B+b+=+8
(2) 40a+%2B+40b+=+320
Subtract (2) from (1)
(1) 40a+%2B+60b+=+440
(2) -40a+-+40b+=+-320
20b+=+120
b+=+6
and, since
(2) a+%2B+b+=+8
a+=+2
2 liters of 40% solution and 6 liters of 60% solution are needed
check answer:
(1) %28.4a+%2B+.6b%29%2F8+=+.55
(1) %28.4%2A2+%2B+.6%2A6%29%2F8+=+.55
%28.8+%2B+3.6%29%2F8+=+.55
4.4%2F8+=+.55
4.4+=+4.4
OK