Question

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.
A) Yes, Chaneece found the correct solution.

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.

C) No, 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.

D) No, 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 1

The answer is B 
No, Chancee mixed up the variables

Answer 2

Chaneece chooses x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions.

y ≤ 40 – x, if x must be between 0 and 10, y must be between 20 and 40 it is true
proof
for x=0  and y=10,  y ≤ 40 – x equivalent to 10<40-0=40 it is true
x=10, y=30,   y ≤ 40 – x  equivalent to 30=40-10=30 it is true

the answer is A) Yes, Chaneece found the correct solution.