Problem of the Week
Problem D and Solution
Healthy Activities
Problem
At UR High School, there are exactly 500 students. Each student must sign-up for either an
aerobics class or a running class. No student can sign-up for both classes. Also, each student
must sign-up for either the Math Club or the Environment Club, but not both. After the
sign-ups were complete, the following information was known: 55% of the students joined the
aerobics class; 68 34 % of the students in the Math Club had also signed up for the aerobics class;
and 40% of the students in the aerobics class were in the Environment Club. Determine the
number of students in the Environment Club who had also signed up for the running class.
Solution
There were 500 students at the school. Since 55% of them joined the aerobics
class, 0.55 ⇥ 500 or 275 students were in the aerobics class. Since all 500
students had to be in either the aerobics class or the running class, it follows
that 500 275 or 225 students were in the running class.
Since 40% of the students in the aerobics class were in the Environment Club,
0.40 ⇥ 275 or 110 students were in both the aerobics class and the Environment
Club. The remainder in the aerobics class, 275 110 or 165 students, were in
the aerobics class and the Math Club.
But these 165 students then represent 68 34 % of the total number of students in
the Math Club. Therefore, 165 ÷ 0.6875 or 240 students were in the Math
Club. It follows that 240 165 or 75 students were in the running class and
the Math Club.
The remaining students had to be in the running class and the Environment
Club. That is, 500 110 165 75 = 150 students are in the running class
and the Environment Club.
TOTAL
165
75
240
110
150
260
275
225
500