A video store rents, on average, 240 videos a day for $2.00 each. The store determined that for every$0.25 that it increases the rental fee, the number of daily rentals will decrease by 10. This relationship can be represented by
y=(240-10n)(2+0.25n) where y is the daily income in dollars from video rentals and n is the number of $0.25 increases. Based on this relationship, at what rental fee per video will the store have its highest daily income? A)$2
B)$4 C)$4.25
D)$7.75 E)$8

SAT2 question:)

The daily income is represented by y, right? If you graph that function (substitute x for n to put it in your calculator), you’ll get a parabola. All you need to do is find the vertex! (Note that, in this problem, you’ll want to do some zooming out.) Don’t want to graph? This is also a great one to backsolve on. Just put each answer choice in
for n and see which one gives you the biggest value for y!

Don’t want to do either of the easy ways? 🙂 Then you’re going to recognize that the equation represents a parabola, and then manipulate it so you can see its roots, and then take the average of the roots to find the n-value for the vertex. Note that doing this requires much more insight into the question than the previous solutions did. So you’ve got roots at –8 and 24. The n-coordinate of the vertex will be smack dab in the middle of those. , so the vertex of the parabola is at n = 8.