15 points
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.

The system of inequalities is x ≥ 3y and x + y ≤ 10

The graph attached down

Step-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

It meand 4 ytjings so with that thatameksbitnhoe eve rnuch it is

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60