Q:

15 points please helpFor a community breakfast there should be at leastthree times as much regular coffee as decaffeinatedcoffee. A total of ten gallons is sufficient for thebreakfast. Write and graph a system of inequalitiesto model the problem.Show your work.

Accepted Solution

A:
Answer:The system of inequalities is x ≥ 3y and x + y ≤ 10The graph attached downStep-by-step explanation:* Lets explain how to write the inequalities for this problem- Assume that x represents the quantity of regular coffee and  y represents the quantity of the decaffeinated  coffee- For a community breakfast there should be at least  three times as  much regular coffee as decaffeinated  coffee- At least means greater than or equal∵ x represents regular coffee∵ y represents decaffeinated  coffee∵ x is at least three times as much as y∴ x ≥ y ⇒ (1)- A total of ten gallons is sufficient for the  breakfast- That means the quantities x and y shouldn't be more than 10- Not more than means smaller than or equal∵ The total quantity is 10 gallons∴ x + y ≤ 10 ⇒ (2)∴ The system of inequalities are    x ≥ 3y and x + y ≤ 10* Lets graph (1) and (2)- The red part for x ≥ 3y- The blue part for x + y ≤ 10