If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 400y?
I. 80
II. 250
III. 399  Options
A) II only	B) III only	C) I and II	D) I and III	E) II and III
We know that x and y are both between 0 and 1.   The minimum limit of 100x + 400y is 100, when x is close to 1 and y is close to 0.   The maximum limit of 100x + 400y is 400, when x is close to 0 and y is close to 1.   The expression can take on any value between 100 and 400.   The answer is II and III.
<result>E</result>
If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 400y?
I. 80
II. 250
III. 399