Hazelnut 8229

There are cherry, hazelnut, and milk candies in a 60-piece candy box. There are 2 times nuttier than cherry and 20 times more milky than nutty. How many candies of each type are in the box?

Correct answer:

m =  36
o =  16
v =  8

Step-by-step explanation:


v+o+m=60
o=2v
m=20+o

v+o+m=60
o=2·v
m=20+o

m+o+v = 60
o-2v = 0
m-o = 20

Row 3 - Row 1 → Row 3
m+o+v = 60
o-2v = 0
-2o-v = -40

Pivot: Row 2 ↔ Row 3
m+o+v = 60
-2o-v = -40
o-2v = 0

Row 3 - 1/-2 · Row 2 → Row 3
m+o+v = 60
-2o-v = -40
-2.5v = -20


v = -20/-2.5 = 8
o = -40+v/-2 = -40+8/-2 = 16
m = 60-o-v = 60-16-8 = 36

m = 36
o = 16
v = 8

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