Problem:
What is the sum of all the solutions of x=∣2x−∣60−2x∣∣?
Answer Choices:
A. 32
B. 60
C. 92
D. 120
E. 124
Solution:
If 60−2x>0, then ∣2x−∣60−2x∣∣=∣4x−60∣. Solving x=4x−60, and x=−(4x−60) results in x=20, and x=12, respectively, both of which satisfy the original equation.
If 60−2x<0, then ∣2x−∣60−2x∣∣=∣2x+60−2x∣=60. Note that x=60 satisfies the original equation. The sum of the solutions is 12+20+60=(C)92.
The problems on this page are the property of the MAA's American Mathematics Competitions