The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chancee choos
es 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 Chancee found the correct solution. If not, state the correct solution.
1 answer:
Answer:
No, Chancee mixed up the variables, the correct solution is that x must be between 20 and 40 and y must be between 0 and 10.
Step-by-step explanation:
Here, x and y are positive integers,
Such that, their sum is not more than 40,
i.e. x + y ≤ 40 where x, y ≥ 0,
⇒ y ≤ 40 - x ...............(1),
Their difference is at least 20,
i.e. x - y ≥ 20
-y ≥ 20 - x
⇒ y ≤ x - 20 ............(2),
Graphing y ≤ 40 - x :
Related equation of inequality (1),
y = 40 - x
if x = 0, y = 40,
if y = 0, 0 = 40 - x ⇒ x = 40,
'≤' represents a solid line,
Join the points (0, 40) and (40, 0) by solid line.
Graphing y ≤ x - 20:
Related equation of inequality (1),
y = x - 20,
if x = 0, y = -20,
if y = 0, 0 = x - 20 ⇒ x = 20,
'≤' represents a solid line,
Join the points (0, -20) and (20, 0) by solid line.
By graphing we obtained a feasible region that is the solution of the system of inequalities (1) and (2) ( shown below ),
In which,
20 ≤ x ≤ 40 and 0 ≤ y ≤ 30
Hence, Chancee did not find the correct solution.
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