Question

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

Answer 1

Answer:

Part A) $15x+25y\geq 700$ and $x> 3y$

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

$15x+25y\geq 700$ ----> inequality A

$x> 3y$ ----> 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

$15x+25y\geq 700$

$15(45)+25(10)\geq 700$

$925\geq 700$ ----> is true

Inequality B

$x> 3y$

$45> 3(10)$

$45> 30$ ----> is true

therefore

The point (45,10) satisfy the system

case 2) (35,15)

For x=35, y=15

Inequality A

$15x+25y\geq 700$

$15(35)+25(15)\geq 700$

$900\geq 700$ ----> is true

Inequality B

$x> 3y$

$35> 3(15)$

$35> 45$ ----> is not true

therefore

The point (35,15) does not satisfy the system

case 3) (30,10)

For x=30, y=10

Inequality A

$15x+25y\geq 700$

$15(30)+25(10)\geq 700$

$700\geq 700$ ----> is true

Inequality B

$x> 3y$

$30> 3(10)$

$30> 30$ ----> is not true

therefore

The point (30,10) does not satisfy the system

case 4) (40,5)

For x=40, y=5

Inequality A

$15x+25y\geq 700$

$15(40)+25(5)\geq 700$

$725\geq 700$ ----> is true

Inequality B

$x> 3y$

$40> 3(5)$

$40> 15$ ----> is true

therefore

The point (40,5)  satisfy the system