Question

A 490 mL IV bag contains a 30% dextrose solution. How much of the original solution must be replaced with a 65% dextrose solution to increase the original concentration to 50%? Round your final answer to 1 decimal place if necessary.

Answer 1

Given:

A 490 mL IV bag contains a 30% dextrose solution.

To find:

How much of the original solution must be replaced with a 65% dextrose solution to increase the original concentration to 50%?

Solution:

Let x mL of the solution is replaced with 65% dextrose solution. So, according to the question:

`\text{ dextrose left in the solution + dextrose in 65\% solution = dextrose in final solution}`

`(520-x)(30)/(100)+x((65)/(100))=520((50)/(100))`

Solve the above equation as follows:

`\begin{gathered} 156-0.3x+0.65x=260 \\ 0.35x=104 \\ x=(104)/(0.35) \\ x=297.1 \end{gathered}`

Thus, 297.1 mL of the 30% dextrose solution must be replaced with 65% dextrose solution.