Answer:
The system of inequalities is x ≥ 3y and x + y ≤ 10
The graph attached down
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