we know that
If a ordered pair is a solution of the combination of carnations and daisies that can be used in the floral arrangement
then
the ordered pair must be in the triangular region graphed and make sense in the context of the situation
using a graphing tool
we're going to proceed to graph and analyze each of the cases
see the attached figure to better understand the problem
Step 1
point [tex]A(6,8.5)[/tex]
The point A is on the triangular region, but the number of daisies is not a whole number
therefore
The ordered pair A does not make sense in the context of the situation
Step 2
point [tex]B(7,5)[/tex]
The point B is on the triangular region, and the number of carnations and daisies are a whole number
therefore
The ordered pair B makes sense in the context of the situation
Step 3
point [tex]C(13,5.6)[/tex]
The point C is on the triangular region, but the number of daisies is not a whole number
therefore
The ordered pair C does not make sense in the context of the situation
Step 4
point [tex]D(12,5)[/tex]
The point D is not on the triangular region
therefore
The ordered pair D does not make sense in the context of the situation
Step 5
point [tex]E(14,7)[/tex]
The point E is on the triangular region, and the number of carnations and daisies are a whole number
therefore
The ordered pair E makes sense in the context of the situation
The answer is
[tex]B(7,5)[/tex]
[tex]E(14,7)[/tex]
