Problem:
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is years. How many years older than Bella is Anna?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The kitten is now years old, and Bella is years old. Thus Anna’s age is years, so Anna is years older than Bella.
Let denote the difference between Anna’s and Bella’s ages. The table below shows the ages of the children and the kitten years ago and today.
The sum of their ages today is so , which gives . Thus Anna is years older than Bella.
Five years ago the combined ages of Anna, Bella, and the kitten was years. Because Bella was years old at the time and the kitten was newborn, Anna must have been years old, so Anna is years older than Bella.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions