SOLUTION: how many litters of 45% saline solution and 70 % saline solution should be mixed to obtain 75 liters of 55 % saline solution?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: how many litters of 45% saline solution and 70 % saline solution should be mixed to obtain 75 liters of 55 % saline solution?      Log On


   

Question 315635: how many litters of 45% saline solution and 70 % saline solution should be mixed to obtain 75 liters of 55 % saline solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(total liters of salt)/(total liters of solution) = 55%
Let a = liters of 45% solution to be added
Let b = liters of 70% solution to be added
given:
(1) a+%2B+b+=+75
.45a+%2B+.7b+=+.55%2A75
.45a+%2B+.7b+=+41.25
(2) 45a+%2B+70b+=+4125
Multiply both sides of (1) by 45 and subtract
(1) from (2)
(2) 45a+%2B+70b+=+4125
(1) -45a+-+45b+=+-3375
25b+=+750
b+=+30
and, since
a+%2B+b+=+75
a+=+45
45 liters of 45% solution must be mixed
with 30 liters of 70% solution