To represent Anna's community service hours in a graphical format, we can define variables for each type of community service:
- Let
represent the number of hours Anna spends on park beautification. - Let
represent the number of hours Anna spends on after-school child care.
From the problem statement, we know:
- Each park beautification session earns her 4 hours, so
where is the number of sessions with park beautification. - Each after-school child care session earns her 2 hours, so
where is the number of sessions with after-school child care.
The total number of community service hours Anna needs to complete is at least 80 hours. Therefore, the inequality can be formulated as:
Substituting in the equations for
To make it simpler for graphing purposes, let's divide the entire inequality by 2:
This equation indicates a linear relationship between the number of park beautification sessions (p) and the number of after-school child care sessions (c). The line
In a graph:
- The x-axis can represent the number of park beautification sessions (p).
- The y-axis can represent the number of after-school child care sessions (c).
- The line would slope down from the point (20, 0) on the p-axis (where 20 sessions of park beautification would give 80 hours) to (0, 40) on the y-axis (where 40 sessions of after-school child care would give 80 hours).
Look for a graph that contains a shaded area above the line