Your students were to determine which plan has the lowest cost given the number of text messages Olamide is likely to send. They were asked to present to Olamide by defining variables, writing equations, making tables, constructing graphs, finding slopes and intercepts and finding points of intersection. Two students came with initial thoughts below, with extra information added in square brackets:

S1: f(x) = 29.95x + 0.10y, f(x) = y + 90.20x, f(x) = 49.95x + 0.05y

[adding extra variable each to the equations and incorrect graph]

S2: x = 29.85 + 10y, x = 90.20, x = 49.95 + 5y,