Problem:
At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
Answer Choices:
A. 161​
B. 203​
C. 31​
D. 2017​
E. 109​
Solution:
21​+41​+101​=2010​+205​+202​=2017​. The rest, 2020​−2017​=203​, walk home.
OR
Since 21​ or 50% of the students use the bus, 41​ or 25% of the students use an auto, and 101​ or 10% of the students use a bicycle, it follows that 100%−(50%+25%+10%)=15% or 203​ of the students walk home.
OR
Assume there are 100 students. This yields
bus50​21​​+automobile25​41​​+bicycle10​101​​+walk15​203​​=100 total.
Thus 15 walk home, which gives 10015​=203​.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions