Problem:
One morning each member of Angela's family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Suppose that the whole family drank cups of milk and cups of coffee. Let denote the number of people in the family. The information given implies that . This leads to
Since and are positive, the only positive integer for which both sides have the same sign is .
\section*{OR}
If Angela drank cups of coffee and cups of mile, then and . The number of people in the family is , which is an integer if and only if . Thus, there are 5 people in the family.
The problems on this page are the property of the MAA's American Mathematics Competitions