Answer:
Part a) The system of two inequalities that describe the situation is
[tex]10x+20y\geq 40[/tex] and [tex]10x+20y\leq 60[/tex]
Part b) Two possible solutions are the points (2,2) and (2,1)
Step-by-step explanation:
step 1
Find the system of inequalities
Let
x------> the number of t-shirts
y----> the number of pants
we know that
[tex]10x+20y\geq 40[/tex] -----> inequality A
[tex]10x+20y\leq 60[/tex] ------> inequality B
using a graphing tool
The solution of the system of inequalities are all positive whole numbers in the shaded area
see the attached figure
step 2
Find two possible solutions
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
Two possible solutions are the points (2,2) and (2,1)
1) (2,2) -------> two t-shirts and two pants
substitute in both inequalities
[tex]x=2,y=2[/tex]
Inequality A
[tex]10(2)+20(2)\geq 40[/tex]
[tex]60 geq 40[/tex] ------> is true
Inequality B
[tex]10(2)+20(2)\leq 60[/tex]
[tex]60\leq 60[/tex] ----> is true
therefore
the ordered pair (2,2) is a possible solution
2) (2,1) -------> two t-shirts and one pant
substitute in both inequalities
[tex]x=2,y=1[/tex]
Inequality A
[tex]10(2)+20(1)\geq 40[/tex]
[tex]40 geq 40[/tex] ------> is true
Inequality B
[tex]10(2)+20(1)\leq 60[/tex]
[tex]40\leq 60[/tex] ----> is true
therefore
the ordered pair (2,1) is a possible solution
