the sum of two positive integers, x and y, is not more than 40. the difference of the two integers is at…

the sum of two positive integers, x and y, is not more than 40. the difference of the two integers is at least 20. chaneece chooses x as the larger number and uses the inequalities y ≤ 40 - x and y ≤ x - 20 to determine the possible solutions. she determines that x must be between 0 and 10 and y must be between 20 and 40. determine if chaneece found the correct solution. if not, state the correct solution.\nyes, chaneece found the correct solution.\nno, chaneece mixed up the variables. the correct solution is that x must be between 20 and 40 and y must be between 0 and 10.\nno, chaneece should not have restricted the solution to quadrant i. the correct solution is that x can be all real numbers and y must be less than 10.\nno, chaneece looked at the wrong area of the shaded graph. the correct solution is that x must be between 0 and 30 and y must be between 0 and 40.

the sum of two positive integers, x and y, is not more than 40. the difference of the two integers is at least 20. chaneece chooses x as the larger number and uses the inequalities y ≤ 40 - x and y ≤ x - 20 to determine the possible solutions. she determines that x must be between 0 and 10 and y must be between 20 and 40. determine if chaneece found the correct solution. if not, state the correct solution.\nyes, chaneece found the correct solution.\nno, chaneece mixed up the variables. the correct solution is that x must be between 20 and 40 and y must be between 0 and 10.\nno, chaneece should not have restricted the solution to quadrant i. the correct solution is that x can be all real numbers and y must be less than 10.\nno, chaneece looked at the wrong area of the shaded graph. the correct solution is that x must be between 0 and 30 and y must be between 0 and 40.

Answer

Explanation:

Step1: Set up inequalities

Given (x + y\leq40) (so (y\leq40 - x)) and (x - y\geq20) (so (y\leq x - 20)), also (x>0,y>0) since (x) and (y) are positive - integers.

Step2: Analyze intersection of inequalities

We consider the system of inequalities. The intersection of (y\leq40 - x) and (y\leq x - 20) along with (x>0,y>0). First, find the intersection of (y = 40 - x) and (y=x - 20). Set (40 - x=x - 20). Adding (x) to both sides gives (40=2x - 20). Adding 20 to both sides: (60 = 2x), so (x = 30). Substituting (x = 30) into (y=x - 20), we get (y = 10). The region defined by (y\leq40 - x), (y\leq x - 20), (x>0) and (y>0) has (x) values such that (20\leq x\leq30) (from (y=x - 20\geq0) and (x + y\leq40)) and (0\leq y\leq10) (from the intersection of the two - line inequalities and non - negativity constraints). Chaneece's solution is incorrect. The correct solution is that (x) must be between 20 and 40 and (y) must be between 0 and 10.

Answer:

B. No, Chaneece mixed up the variables. The correct solution is that (x) must be between 20 and 40 and (y) must be between 0 and 10.