Mixed motives (math)

Imagine you have two reasons for wanting to do something. One reason is to help someone else and the other reason is to get something for yourself. This is what we call "mixed motives."

In math, mixed motives can happen when we have two or more factors that are causing something to happen, and we need to figure out how much each of those factors is contributing. For example, imagine you're trying to figure out why a plant is growing so well. Maybe it's because it's getting a lot of sunlight, but also because it's getting just the right amount of water. How much of the plant's growth is due to the sunlight and how much is due to the water? That's what we need to figure out when we're dealing with mixed motives in math.

To figure out the contributions of each factor, we might use something called "proportions." Think of it like baking a cake: if you have a recipe that calls for 1 cup of flour and 2 eggs, you can figure out how much flour you need if you know how many eggs you have. In the same way, if we know how much a plant grows with just one factor (say, sunlight), we can figure out how much it grows with both factors by using proportions.

So, mixed motives might sound complicated, but they just mean that there are multiple reasons for something happening, and we need to figure out how much each reason is "contributing" to the overall result.