I often find students who dislike algebra. They prefer to work with numbers in solving problems. I believe there are many problems that are hard to solve without algebra. For example:
Finding the value of $x$ such that the volume of a box without lid reaches a maximum value.
A tank contains 40 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing half water and half alcohol is added to the tank at the rate of 4 gallons per minute. At the same time, the tank is being drained at the rate of 4 gallons per minute, as shown in below. Assuming that the solution is stirred constantly, how much alcohol will be in the tank after 10 minutes?
Could you provide me with other simple "interesting and challenging" examples so I can introduce them to my students?