# A chemist mixes a 10% saline solution with a 20% saline solution to make 500 milliliters of a 16% saline solution. How many milliliters of each solution does the chemist mix together?

##### 2 Answers

#### Explanation:

To solve for two unknowns we need two equations/pieces of information. Our two unknowns are the volumes of each stock solution. Let:

For our first equation, we know the total volume is 500 mL and is the sum of x and y:

For our second equation, we do a mass balance for 500 mL of final solution.

This means that in 1 mL of solution, we have 0.16 g of NaCl.

For any solution, concentration multiplied by volume will give the mass of NaCl:

So in

So, the sum of the masses of NaCl in

Now, substitute our expression for x, (1), into (2):

Now solve for y using (1):

A different approach! Very detailed explanation given.

For the 20% constituent:

For the 10% constituent:

#### Explanation:

The total volume is a fixed amount. So if the proportion of the 20% concentration is known then the amount of 10% solution is:

Thus by just focusing on the 20% the amount of the 10% is indirectly linked. Thus in this approach we can (sort of) forget about the amount of 10% mix.

By varying the amount of the 20% mix the saline content of the whole changes. It is this change that we are looking at.

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Let the proportion of the 20% solution be

The gradient of part is the same as the gradient of the whole.

Using ratio:

Giving

Multiply both sides by 6

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Thus there is:

Check:

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For the 20% constituent:

For the 10% constituent: