If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 700y?
I. 90
II. 250
III. 699 Choose one: 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 + 700y is 100, when x is close to 1 and y is close to 0.   The maximum limit of 100x + 700y is 700, when x is close to 0 and y is close to 1.   The expression can take on any value between 100 and 700.   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 + 700y?
I. 90
II. 250
III. 699