Candies in the jug

In the jug there are candies.
The first taker of candy was Lukáš, who took a certain number. The second taker was Zuzka, who took twice as many candies as Jirka; at that moment there were 0 candies in the jug. How many did each of them take, if the number of candies taken by Zuzka and Jirka equalled the candies taken by Lukáš. We will also hint that at the beginning there were 60 candies in the jug.

Final Answer:

j =  10
l =  30
z =  20

Step-by-step explanation:

l+j+z = 60
z = 2j
z+j=l

l+j+z = 60
z = 2·j
z+j=l

j+l+z = 60
2j-z = 0
j-l+z = 0

Pivot: Row 1 ↔ Row 2
2j-z = 0
j+l+z = 60
j-l+z = 0

Row 2 - 1/2 · Row 1 → Row 2
2j-z = 0
l+1.5z = 60
j-l+z = 0

Row 3 - 1/2 · Row 1 → Row 3
2j-z = 0
l+1.5z = 60
-l+1.5z = 0

Row 3 + Row 2 → Row 3
2j-z = 0
l+1.5z = 60
3z = 60


z = 60/3 = 20
l = 60-1.5z = 60-1.5 · 20 = 30
j = 0+z/2 = 0+20/2 = 10

j = 10
l = 30
z = 20

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