This is a good question. How does algebra help me in the real world? There are several ways in which to answer this question. Let me give you two points.
First, whenever you use your mind in solving equations, it is a good thing. The reason for his is simple; problem solving exercises your mind. You become more intelligent and this general intelligence can be used in other areas.
Second, the process of elimination is perfect for the medical profession, because much of medicine is based on the process of elimination. Medicine is not always an exact science, as one might believe. You need to rule things out and then come to a proper diagnosis based on the available facts. So, in this sense algebra would be very helpful.