Question

The applications of systems of equations exist in a wide variety of ways. From our early encounters of a system of equations involved with cooking ingredients to our numerous adventures into the business world where system of equations lead to a company's prosperity, the consistent theme throughout this section is that systems of equations are intertwined with many aspects of our life. As a result, you are tasked with providing an example in your own life where you could have used a system of equations to solve a problem in your everyday life (outside of the classroom setting). You will need to provide the scenario along with the corresponding system of equations for your given scenario.  

1. Provide a scenario where you could have used a system of equations to solve a real world problem.
2. Provide a system of equations that is associated with your real world problem.
3. Reply to a classmate with the steps towards finding a solution to their problem along with the final solution.

Answer 1

As a fun part during playing, we decided to sit on the seesaw in such a way that the seesaw will not go up or down, rather it will just stay at equilibrium horizontally. For that, we needed to calculate at what distances the two persons needed to sit from the center of the seesaw so that the seesaw is in equilibrium. We can use the moment equation to calculate the ratio of the distances at which two persons of mass m1 and m2 should sit so that the total moment is zero. We can write,

(l1 and l2 are the distances from the center at which the person with mass m1 and m2 are sitting.)

By keeping up with this ratio we were able to keep the seesaw in balance and it stayed horizontally there.