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

2 Answers
Tazwar Sikder
Sep 17, 2017

22 "qt."qt.

Explanation:

Let xx and yy be the number of "qt."qt. of the 90%90% solution and the number of "qt."qt. of 45%45% solution, respectively.

We can then express the problem mathematically as:

Rightarrow x + 3 = y⇒x+3=y

oror

Rightarrow x⇒x "qt. of"qt. of 90%90% "solution"solution + 3+3 "qt. of"qt. of 15%15% "solution"solution == yy "qt. of"qt. of 45%45% "solution"solution

Rightarrow x times 0.90 + 3 times 0.15 = y times 0.45⇒x×0.90+3×0.15=y×0.45

Rightarrow 0.90 x + 0.45 = 0.45 y⇒0.90x+0.45=0.45y

Rightarrow 0.90 x = 0.45 y - 0.45⇒0.90x=0.45y−0.45

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

Rightarrow 0.90 x = 0.45 (x + 3) - 0.45⇒0.90x=0.45(x+3)−0.45

Rightarrow 0.90 x = 0.45 x + 1.35 - 0.45⇒0.90x=0.45x+1.35−0.45

Rightarrow 0.45 x = 0.90⇒0.45x=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.

Shwetank Mauria
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 3qt. 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.

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