You have to use algebraic thinking, but you don't have to use an equation. We are never asked about the price of the individual pairs of shoes, so it doesn't matter that there are three pair. We can ignore it.
- The handbag and the shoes cost $324 total together.
- The handbag costs half as much as the shoes (example, the shoes cost $100 and the handbag costs $50)
So, for every dollar we spend on the handbag, we spend two dollars on the shoes and $3 total. (If this doesn't make sense, try drawing a diagram).
We need to divide the $324 by 3 because there a three parts: 1 part handbag and 2 parts shoes.
We spend $108 on the handbag and $216 on the 3 pairs of shoes.