Problem:
Jami picked three equally spaced integer numbers on the number line. The sum of the first and the second numbers is , while the sum of the second and third numbers is . What is the sum of all three numbers?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the middle number on the number line be represented by . Let the distance between the middle number to the other two numbers be represented by . We therefore get the following equations:
and
From the first equation, we get:
From the second equation, we get:
Adding these equations, we get , and from there, we get . Because the numbers are equally spaced, the average of the numbers is . Hence, the total sum of the numbers is .
The problems on this page are the property of the MAA's American Mathematics Competitions