Mrs. Burgos wants to buy at least 30 kilos of pork and beef for her restaurant business but has to spend no more than Php 12000.A
kilo of pork costs Php 180 and a kilo of beef costs Php 220. What
mathematical statements (system of inequalities) represent the
situation? Determine if each of the ordered pairs is a solution or not
to the system of inequalities: (40,10), (20,5), (50,20).

We want to write a system of inequalities that models the given situation.

The system is:

x*180 + y*220 ≤ 12,000

x + y ≥ 30

And from the given points, the only one that is a solution is (40, 10).

The first thing we must do, is to define the variables we will be using.

Then the cost is given by:

x*180 + y*220

And this must be no more than 12,000

Then we have the inequality:

x*180 + y*220 ≤ 12,000

We also know that he wants to buy at least 30 kilos of pork and beef, then we have:

x + y ≥ 30

Then the system of inequalities is:

x*180 + y*220 ≤ 12,000

x + y ≥ 30

Now we want to see which of the given points is a solution of the system, to see this, we just need to evaluate the points in each inequality.

For the first point we have:

x = 40

y = 10

40*180 + 10*220 = 9,400 ≤ 12,000

40 + 10 = 50 ≥ 30

So (40, 10) is a solution.

For the second point:

x = 20

y = 5

notice that:

20 + 5 = 25 ≥ 30    (this is false, so (20, 5) is not a solution).

For the third point we have:

x = 50

y = 20

50*180 + 20*220 = 13,400 ≤ 12,000  (this is false, so the point is not a solution)

Then the only solution is (40,10).

If you want to learn more, you can read:

link

The attached graph shows the solution.

Point (40,10) is a solution to the system of inequalities.

Step-by-step explanation:

Let pork be represented byx

Let beef be represented byy

Burgos wants to buy at least 30 kilos of pork and beef, which means the kilos to buy can be 30 kg or more. This can be written as inequality equation into ;

x+y ≥ 30 1

The amount to spend is no more than Php 12000, which means the maximum amount to spend is Php 12000 or less.

and if : A  kilo of pork costs Php 180 and a kilo of beef costs Php 220 then the inequality for total cost will be:

180 x + 220 y ≤ 12000 2

So the two inequality equation to solve are :

x+y ≥ 30

180 x + 220 y ≤ 12000

Using a graph tool to graph the inequalities and view the solution will give the shaded part (center part) with point (40,10).

The other points (20,5), (50,20) are out of the area (center shaded part) that satisfy the inequalities, thus not a solution.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!