Problem:
Oscar buys 13 pencils and 3 erasers for . A pencil costs more than an eraser, and both items cost a whole number of cents. What is the total cost, in cents, of one pencil and one eraser?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the cost (in cents) of a pencil, and let be the cost (in cents) of a set of one pencil and one eraser. Because Oscar buys 3 sets and 10 extra pencils for , we have
Thus is a multiple of 10 that is less than 100 , so is 10,20 , or 30 . The corresponding values of are 7,4 , and 1 . Since the cost of a pencil is more than half the cost of the set, the only possibility is .
The problems on this page are the property of the MAA's American Mathematics Competitions