Strawberry picking reward

For picking strawberries, the girls divided the reward of CZK 15,100 according to their performance. Lucy received CZK 400 more than Šárka, Jana half of what Lucy and Šárka got together, and Kamila CZK 500 less than Jana. How many CZK did each girl get? (Solution and procedure word problem)

Final Answer:

j = 3900
k = 3400
l = 4100
s = 3700

Step-by-step explanation:

l=400+s
j = (l+s)/2
k = j - 500
j+k+s+l=15100

l-s = 400
2j-l-s = 0
j-k = 500
j+k+l+s = 15100

Pivot: Row 1 ↔ Row 2
2j-l-s = 0
l-s = 400
j-k = 500
j+k+l+s = 15100

Row 3 - 1/2 · Row 1 → Row 3
2j-l-s = 0
l-s = 400
-k+0.5l+0.5s = 500
j+k+l+s = 15100

Row 4 - 1/2 · Row 1 → Row 4
2j-l-s = 0
l-s = 400
-k+0.5l+0.5s = 500
k+1.5l+1.5s = 15100

Pivot: Row 2 ↔ Row 3
2j-l-s = 0
-k+0.5l+0.5s = 500
l-s = 400
k+1.5l+1.5s = 15100

Row 4 + Row 2 → Row 4
2j-l-s = 0
-k+0.5l+0.5s = 500
l-s = 400
2l+2s = 15600

Pivot: Row 3 ↔ Row 4
2j-l-s = 0
-k+0.5l+0.5s = 500
2l+2s = 15600
l-s = 400

Row 4 - 1/2 · Row 3 → Row 4
2j-l-s = 0
-k+0.5l+0.5s = 500
2l+2s = 15600
-2s = -7400

s = -7400/-2 = 3700
l = 15600-2s/2 = 15600-2 · 3700/2 = 4100
k = 500-0.5l-0.5s/-1 = 500-0.5 · 4100-0.5 · 3700/-1 = 3400
j = 0+l+s/2 = 0+4100+3700/2 = 3900

j = 3900
k = 3400
l = 4100
s = 3700

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