# Question #1037e

##### 1 Answer

Here's what I got.

#### Explanation:

You would pick a sample of the stock solution and dilute it.

For example, let's say that you start with a

#100.0color(red)(cancel(color(black)("mL"))) * (4.5 * 10^8"cells")/(1color(red)(cancel(color(black)("mL")))) = 4.5 * 10^(10)"cells"#

Now, when you're diluting this solution, you're essentially keeping the number of cells **constant** and changing the volume of the solution.

The concentration of the cells will change **not** because the number of cells change, but because the **volume** of the solution changes.

So, what volume would you need to have in order for

#4.5 * 10^10color(red)(cancel(color(black)("cells"))) * "1 mL"/(4.5 * 10^4color(red)(cancel(color(black)("cells")))) = 10^6"mL"#

This means that you must add enough water to your initial

**SIDE NOTE** *To make the calculations a little easier, pick an original sample of* *You would have* *cells in this sample*. *The volume of the final sample would be*

#4.5 * 10^8color(red)(cancel(color(black)("cells"))) * "1 mL"/(4.5 * 10^4color(red)(cancel(color(black)("cells")))) = 10^4"mL"#

*Therefore, you must add enough water to the original* *sample to make the total volume equal to*