A fifth-grade teacher brought some papers home to grade over the weekend. Each English paper takes
1
4
of an hour to grade, and each math test takes
1
6
of an hour to grade. The teacher wants to spend over 3 hours but under 6 hours on grading this weekend.
Graph a system of inequalities that represents this story. One inequality should represent the minimum number of hours the teacher wants to spend grading, and the other inequality should represent the maximum number of hours she wants to spend grading.
Select a line to change it between solid and dotted. Select a region to shade it.
The inequalities can be represented as follows:
Let E represent the number of English papers and M represent the number of math tests.
Minimum time constraint:
1/4E + 1/6M ≥ 3
Maximum time constraint:
1/4E + 1/6M < 6
To graph these inequalities, we first need to rewrite them in slope-intercept form:
Minimum time constraint:
M ≥ -4/6E + 18
Maximum time constraint:
M < -4/6E + 24
Now, we can graph the system of inequalities on a coordinate plane. The minimum time constraint line will be solid, and the shaded region will be above it. The maximum time constraint line will be dashed, and the shaded region will be below it.
I'm sorry, but I am unable to draw the graph here. Please try plotting these inequalities on a graphing tool or by hand to visualize the solution set.