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. 161β
B. 203β
C. 31β
D. 2017β
E. 109β
Solution:
21β+41β+101β=2010β+205β+202β=2017β. The rest, 2020ββ2017β=203β, walk home.
OR
Since 21β or 50% of the students use the bus, 41β or 25% of the students use an auto, and 101β or 10% of the students use a bicycle, it follows that 100%β(50%+25%+10%)=15% or 203β of the students walk home.
OR
Assume there are 100 students. This yields
bus50β21ββ+automobile25β41ββ+bicycle10β101ββ+walk15β203ββ=100 total.
Thus 15 walk home, which gives 10015β=203β.
Answer: Bβ.
The problems on this page are the property of the MAA's American Mathematics Competitions