Pytagoriade

Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed in the Mathematical Olympiad. Students who competed in both competitions was 4 times more than those who only competed in Pytagoriade.

a) How many students competed in both competitions?
b) How many students competed in just one competition?
c) How many students competed in no more than one competition?

Correct result:

a =  16
b =  6
c =  17

Solution:

p+a+o = 22
p = 2 o
a = 4p
b = p+o
c = 33-a


p+a+o = 22
p = 2•o
a = 4•p
b = p+o
c = 33-a

a+o+p = 22
2o-p = 0
a-4p = 0
b-o-p = 0
a+c = 33

a = 16
b = 6
c = 17
o = 2
p = 4

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