Under her Dinner budget category, Diane allocated $600 per month for eating in and dining out. She figures that eating in will cost her approximately $8 and dining out will cost her approximately $24. Let x represent the number of dinners eaten in, and y represent the number of dinners eaten out.
a. Determine a budget line equation for this situation.
b. In a typical 30-day month, the sum of the dinners eaten in and out must be less than or equal to 30. Write the budget equation for the exact number of dinners for the month.
c. Graph the budget line and the equation from part b on the same axes.
d. Based on the graph, name a combination of dinners eaten in and out that will allow her to be within her Dinner budget.
e. Name a combination of dinners that will cause her to be over budget.