My son was confused today by a percent problem from Art of Problem Solving’s Algebra book. I liked the problem a lot and thought talking through it would be really helpful for him.

Here’s the introduction to the problem plus some initial steps – he is really confused about how to get going with the problem. His initial thought is to combine equal amounts. That gets us going, but he struggles to see where to go after that:

At the end of the last video we were still a little stuck. He knows that we need more than 1 cup of the mixture with more fat and less than one cup of the mixture with less fat. Our first try here is a new split – 1.5 cups and 0.5 cups. This mixture turns out to have too much fat, but it does help us understand the problem a bit better.

To finish up the conversation today we summarized what we’d done so far. That gave him the idea to try a split of 1.25 and 0.75. This split got us to the right answer. We’ll revisit this problem again to see how algebra can help us solve it.