MATH SOLVE

3 months ago

Q:
# Given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation

Accepted Solution

A:

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 systemStep-by-step explanation:Part A) Determine which inequalities represent the constraints for this situationLetx -----> the number of small prints soldy -----> the number of large prints soldwe know thatThe system of inequalities that represent this situation is equal to[tex]15x+25y\geq 700[/tex] ----> inequality A[tex]x> 3y[/tex] ----> inequality BPart B) With combinations of small prints and large prints satisfy this system?we know thatIf a ordered pair is a solution of the system, then the ordered pair must satisfy both inequalitiesVerify each casecase 1) (45,10)For x=45, y=10Inequality A[tex]15x+25y\geq 700[/tex] [tex]15(45)+25(10)\geq 700[/tex] [tex]925\geq 700[/tex] ----> is trueInequality B[tex]x> 3y[/tex][tex]45> 3(10)[/tex][tex]45> 30[/tex] ----> is truethereforeThe point (45,10) satisfy the systemcase 2) (35,15)For x=35, y=15Inequality A[tex]15x+25y\geq 700[/tex] [tex]15(35)+25(15)\geq 700[/tex] [tex]900\geq 700[/tex] ----> is trueInequality B[tex]x> 3y[/tex][tex]35> 3(15)[/tex][tex]35> 45[/tex] ----> is not truethereforeThe point (35,15) does not satisfy the systemcase 3) (30,10)For x=30, y=10Inequality A[tex]15x+25y\geq 700[/tex] [tex]15(30)+25(10)\geq 700[/tex] [tex]700\geq 700[/tex] ----> is trueInequality B[tex]x> 3y[/tex][tex]30> 3(10)[/tex][tex]30> 30[/tex] ----> is not truethereforeThe point (30,10) does not satisfy the systemcase 4) (40,5)For x=40, y=5Inequality A[tex]15x+25y\geq 700[/tex] [tex]15(40)+25(5)\geq 700[/tex] [tex]725\geq 700[/tex] ----> is trueInequality B[tex]x> 3y[/tex][tex]40> 3(5)[/tex][tex]40> 15[/tex] ----> is truethereforeThe point (40,5) satisfy the system