How much #90%# saline solution should we mix to #3qt.# of #15%# saline mix to make #45%# saline solution?

2 Answers
Sep 17, 2017

#2# #"qt."#

Explanation:

Let #x# and #y# be the number of #"qt."# of the #90%# solution and the number of #"qt."# of #45%# solution, respectively.

We can then express the problem mathematically as:

#Rightarrow x + 3 = y#

#or#

#Rightarrow x# #"qt. of"# #90%# #"solution"# #+ 3# #"qt. of"# #15%# #"solution"# #=# #y# #"qt. of"# #45%# #"solution"#

#Rightarrow x times 0.90 + 3 times 0.15 = y times 0.45#

#Rightarrow 0.90 x + 0.45 = 0.45 y#

#Rightarrow 0.90 x = 0.45 y - 0.45#

Then, let's substitute the first mathematical expression in place of #y#:

#Rightarrow 0.90 x = 0.45 (x + 3) - 0.45#

#Rightarrow 0.90 x = 0.45 x + 1.35 - 0.45#

#Rightarrow 0.45 x = 0.90#

#therefore x = 2#

Therefore, we need to mix #2# #"qt."# of the #90%# saline solution with #3# #"qt."# of #15%# saline solution to make a #45%# solution.

Sep 17, 2017

We need #2# qt. of #90%# saline solution.

Explanation:

Let us assume that we need to mix #x# qt. of #90%# saline solution. It will have #x xx90/100=0.9x# qt. saline.

It is mixed with #3#qt. of #15%# saline solution, this as #3xx15/100=0.45# qt. saline

and on mixing the two, the total quantum of saline is #0.9x+0.45# qt.

This is #45%# of #x+3# or #(x+3)xx0.45#

hence #0.45(x+3)=0.9x+0.45#

or #0.45x+1.35=0.9x+0.45#

or #0.9x-0.45x=1.35-0.45#

or #0.45x=0.9#

i.e. #x=0.9/0.45=2#

Hence, we need #2# qt. of #90%# saline solution.