Rings groups

Twenty-seven pupils attend some groups. Fourteen pupils attend the Dance group, 21 sports group, and 16 in the dramatic group. Dance and sporting attend nine pupils, dance and drama six pupils, sporty and dramatic 11 pupils. How many pupils attend all three groups?

Correct answer:

o =  -1

Step-by-step explanation:


a+b+c+x+y+z+o=27
a+x+y+o=14
b+x+z+o=21
c+y+z+o=16
x=9
y=6
z=11

a+b+c+o+x+y+z = 27
a+o+x+y = 14
b+o+x+z = 21
c+o+y+z = 16
x = 9
y = 6
z = 11

Row 2 - Row 1 → Row 2
a+b+c+o+x+y+z = 27
-b-c-z = -13
b+o+x+z = 21
c+o+y+z = 16
x = 9
y = 6
z = 11

Row 3 + Row 2 → Row 3
a+b+c+o+x+y+z = 27
-b-c-z = -13
-c+o+x = 8
c+o+y+z = 16
x = 9
y = 6
z = 11

Row 4 + Row 3 → Row 4
a+b+c+o+x+y+z = 27
-b-c-z = -13
-c+o+x = 8
2o+x+y+z = 24
x = 9
y = 6
z = 11


z = 11/1 = 11
y = 6/1 = 6
x = 9/1 = 9
o = 24-x-y-z/2 = 24-9-6-11/2 = -1
c = 8-o-x/-1 = 8+1-9/-1 = -0
b = -13+c+z/-1 = -13+11/-1 = 2
a = 27-b-c-o-x-y-z = 27-2+1-9-6-11 = 0

a = 0
b = 2
c = -0
o = -1
x = 9
y = 6
z = 11

Our linear equations calculator calculates it.



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