Answer:
Part A) [tex]15x+25y\geq 700[/tex] and [tex]x> 3y[/tex]
Part B) The point (45,10) and the point (40,5) satisfy the system
Step-by-step explanation:
Part A) Determine which inequalities represent the constraints for this situation
Let
x -----> the number of small prints sold
y -----> the number of large prints sold
we know that
The system of inequalities that represent this situation is equal to
[tex]15x+25y\geq 700[/tex] ----> inequality A
[tex]x> 3y[/tex] ----> inequality B
Part B) With combinations of small prints and large prints satisfy this system?
we know that
If a ordered pair is a solution of the system, then the ordered pair must satisfy both inequalities
Verify each case
case 1) (45,10)
For x=45, y=10
Inequality A
[tex]15x+25y\geq 700[/tex]
[tex]15(45)+25(10)\geq 700[/tex]
[tex]925\geq 700[/tex] ----> is true
Inequality B
[tex]x> 3y[/tex]
[tex]45> 3(10)[/tex]
[tex]45> 30[/tex] ----> is true
therefore
The point (45,10) satisfy the system
case 2) (35,15)
For x=35, y=15
Inequality A
[tex]15x+25y\geq 700[/tex]
[tex]15(35)+25(15)\geq 700[/tex]
[tex]900\geq 700[/tex] ----> is true
Inequality B
[tex]x> 3y[/tex]
[tex]35> 3(15)[/tex]
[tex]35> 45[/tex] ----> is not true
therefore
The point (35,15) does not satisfy the system
case 3) (30,10)
For x=30, y=10
Inequality A
[tex]15x+25y\geq 700[/tex]
[tex]15(30)+25(10)\geq 700[/tex]
[tex]700\geq 700[/tex] ----> is true
Inequality B
[tex]x> 3y[/tex]
[tex]30> 3(10)[/tex]
[tex]30> 30[/tex] ----> is not true
therefore
The point (30,10) does not satisfy the system
case 4) (40,5)
For x=40, y=5
Inequality A
[tex]15x+25y\geq 700[/tex]
[tex]15(40)+25(5)\geq 700[/tex]
[tex]725\geq 700[/tex] ----> is true
Inequality B
[tex]x> 3y[/tex]
[tex]40> 3(5)[/tex]
[tex]40> 15[/tex] ----> is true
therefore
The point (40,5) satisfy the system
