Question

A nurse mixes 40 cc of a 70% saline solution with a 10% saline solution to produce a 26% saline solution. How much of the 10% solution should he use?

Answer 1

ANSWER :

He should use 110 cc of 10% solution

EXPLANATION :

Note that the percent solution is the amount of salt divided by the total volume or quantity.

From the problem, 40 cc of a 70% saline solution.

The amount of salt is 0.70(40) = 28 cc

Another solution is "x" cc of 10% saline solution.

The amount of salt is 0.10x cc

When added together, the total volume is 40 + x

and the amount of salt is 28 + 0.10x

The resulting solution is 26% saline solution.

So we can have :

$\frac{\text{ amount of salt}}{\text{ total volume}}=0.26$

Substitute the results :

$\begin{gathered} \frac{28+0.10x}{40+x}=0.26 \\ \text{ Cross multiply :} \\ 28+0.10x=0.26(40+x) \\ 28+0.10x=10.4+0.26x \\ 0.10x-0.26x=10.4-28 \\ -0.16x=-17.6 \\ x=\frac{-17.6}{-0.16}=110 \end{gathered}$