How to think about "Mixture" Problems

Math Student Teaching Spring 2000

Pat Thompson, Vanderbilt University

We want to make 300 g of a salt solution containing 6% salt. We will make it by pouring together two other salt solutions, one containing 8% salt and the other containing 5% salt. How many grams of the 5% solution and how many grams of the 8% solutions should we mix?


Things to notice about the problem



We can organize our understanding of this problem as such:

Start off with two mixtures:

Combine them to make a new mixture


Things we can deduce from the information in this problem




We can use a table to organize our thinking


  1. We know we will have 300 grams of solution that is 6% salt.
  2. 300 grams of solution that is 6% salt contains 18 grams of salt.
  3. Assume we have x grams of 8% solution.
  4. x grams of solution that is 8% salt will contain .08x grams of salt.
  5. Since there are 18 grams of salt altogether and .08x grams of it comes from the 8% solution, the rest of it, 18-.08x grams, must come from the 5% solution.
  6. For the 5% solution to be 5% salt, the entire amount of solution must weigh 20 times as much as the salt in it. Therefore, there is 20(18-.08x) grams of 5% solution.
  7. The two amounts of solution must total 300 grams when combined. Therefore,
    300 = x + 20(18 - .08x).


We can generalize this understanding

(after having solved several problems like this)


Start off with two amounts of two mixtures


Combine them to make a new mixture


Use a table to organize your thinking