Problem:
In the fall of 1996, a total of 800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997,1998, and 1999, participation will increase by 50% over the previous year. The number of participants the organizers expect in the fall of 1999 is
Answer Choices:
A. 1200
B. 1500
C. 2000
D. 2400
E. 2700
Solution:
Since 50% of 800 is 400, the organizers expect 800+400=1200 participants in 1997. Since 50% of 1200 is 600,1200+600=1800 are expected in 1998. Since 50% of 1800 is 900,1800+900=2700 are expected in 1999.
OR
Make a table.
YEAR1996199719981999​NUMBER OF PARTICIPANTS800800+(0.5×800)=12001200+(0.5×1200)=18001800+(0.5×1800)=2700​​
OR
An increase of 50% means there will be 100%+50% or 1.5 times as many participants in each successive year. Thus in 1999, three years from 1996, there will be 800×1.53=2700 participants.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions