A two-variable inequality models a limit on combinations of two kinds of work. Convert all times to minutes, subtract time that can't be spent working, and multiply each task's time by its count. Graph the resulting inequality in Desmos to see the allowed side. The trap is that within the available time means no more than the limit, not at least the limit.
Hints
- Hint 1
Put both times in minutes before comparing them. An hour has 60 minutes, and the meeting uses part of the desk time. How many minutes remain for returns?
- Hint 2
The total processing time is the time for each kind of return multiplied by its count, then added. Keep the paperback time with and the hardcover time with .
- Hint 3
Finishing within the available time includes finishing exactly at the limit. Should the total processing time be less than or equal to that limit, or greater than or equal to it?
Step-by-step
Build the time-limit inequality
Step 1Find the time left for returns
The meeting takes away desk time. An hour has minutes, so type in Desmos. It prints , the number of minutes available for processing returns.
- Step 2
Write the total processing time
Each paperback takes minutes, so paperbacks take minutes. Each hardcover takes minutes, so hardcovers take minutes. Add them to get the total processing time: . Swapping the rates would assign the wrong time to each kind of return.
- Step 3
Set the time limit
The phrase within her available time means the total can be no more than the time left, including exactly that amount: . Type in Desmos. It shades the allowed side of a solid boundary line; only nonnegative whole-number pairs in that shading represent counts of returns. So models the combinations she can complete. Choice D.