Brain Teasers
Room Seats
If 18 students occupy 3/5 of the seats in the classroom, how many students would
occupy 2/3 of the seats in the room?
This brainteaser was supplied
by the Mathematical Olympiads for Elementary and Middle Schools (www.moems.org).
Solution: 20.
One
approach is to use algebra to find the answer. If there are n seats in the room, then an equation can be solved as follows:
Consequently,
if there are 30 seats, then (2/3)×30=20 students would fill 2/3 of the seats.
A
more intuitive approach might involve a visual representation. If 3/5 of the
classroom is 18 seats, then the entire classroom, or 5/5, must be 30 seats, as
shown below:
Another
visual representation can be used to show that 2/3 of the classroom is 20
seats.
Finally,
a purely numeric solution relies on the fact that 3/5 is equivalent to 18/30,
which implies that there are 30 seats in the classroom. Then 2/3 × 30 = 20
seats.
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