Making Decisions on Sculptures for Event Decoration
What system of inequalities models the scenario where Martin, an event planner, needs to order sculptures for a wedding venue within a budget of $1,591 and a minimum requirement of 13 sculptures?
A) $58x + $245y ≥ $1,591, where x represents the number of small sculptures and y represents the number of large sculptures.
B) $245x + $58y ≤ $1,591, where x represents the number of small sculptures and y represents the number of large sculptures.
C) $58x + $245y ≤ $1,591, where x represents the number of small sculptures and y represents the number of large sculptures.
D) $58x + $245y = $1,591, where x represents the number of small sculptures and y represents the number of large sculptures.
Answer:
The system of inequalities that best represents the scenario is C) $58x + $245y ≤ $1,591 and x+y ≥ 13, where x represents the number of small sculptures and y represents the number of large sculptures. The correct option is C.
In the scenario described, Martin, an event planner, is tasked with making decisions regarding sculptures for decorating a wedding venue within a specified budget and quantity requirement. To ensure the choices he makes align with these restrictions, a system of inequalities needs to be set up.
If we assign 'x' as the number of small sculptures and 'y' as the number of large sculptures, the correct system of inequalities would be: C) $58x + $245y ≤ $1,591, indicating that the total cost of the small and large sculptures should not exceed $1,591, and x+y ≥ 13 because Martin needs a minimum of 13 sculptures regardless of their size. This system captures the fact that small sculptures cost $58 each and large sculptures cost $245 each.
By adhering to these inequalities, Martin can effectively manage his budget while ensuring that the wedding venue is elegantly decorated with the appropriate number of sculptures. This strategic approach allows him to make informed decisions based on financial constraints and quantity requirements.