76.3k views
1 vote
15 points please help

For a community breakfast there should be at least
three times as much regular coffee as decaffeinated
coffee. A total of ten gallons is sufficient for the
breakfast. Write and graph a system of inequalities
to model the problem.
Show your work.

1 Answer

4 votes

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

15 points please help For a community breakfast there should be at least three times-example-1
User Vlad Patryshev
by
8.8k points