A lot of times the applications we come across for algebraic topics feel contrived; here’s one that occurred naturally in my very own home yesterday.
My wife works in a clinic with two other midwives. They all do the same amount of “on-call” time, but have different workloads when it comes to clinic hours. And sometimes they’re on call while they’re in the clinic. She knows their salaries, but didn’t know the hospital’s pay rate for clinic hours, on-call hours, or combo hours – she was interested in finding this out to see if it was worthwhile to pick up some extra shifts at the clinic.
Calling the number of on-call hours X, the number of clinic hours Y, and the number of combo hours Z, she set up an equation for each midwife and was able to figure out the pay rate for each type of work.
Math to the rescue!