This problem is typical of the earliest algebra problems that likely came out of India. It is interesting historically, and it is the kind of problem students are still taught to solve today. We can do it very differently using spreadsheets.
Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general form is f(x)=mx+b where m is the slope of the function and b is the y-intercept, the value where the line crosses the y-axis. This Lab is designed to give you a picture of a linear function based on its formula. So play with it until you can picture the function from its formula and its formula from its graph.
Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will focus mainly on climate change which is an area rich in possibilities and of great interest to students. In this case study we look at the production of carbon dioxide per person in the United States over the past 200 years. We take this opportunity to introduce students to the difference between quantity and growth, between the amount of CO2 produced and the year-to-year growth in production. We challenge students to consider whether this growth is an increasing problem.