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.
Let x be the number of English papers to grade and y be the number of math tests to grade.
The time it takes to grade x English papers is 1/4x hours.
The time it takes to grade y math tests is 1/6y hours.
The teacher wants to spend over 3 hours but under 6 hours grading, so the inequalities are:
1/4x + 1/6y >= 3 (minimum number of hours)
1/4x + 1/6y <= 6 (maximum number of hours)
The graph of the system of inequalities would look like this:
The minimum number of hours line: 1/4x + 1/6y = 3 (solid line)
The maximum number of hours line: 1/4x + 1/6y = 6 (solid line)
The shaded region between the two lines represents the range of hours the teacher wants to spend grading.