Strawberry picking reward

For picking strawberries, the girls divided a reward of CZK 15,100 according to their performance. Lucy received CZK 400 more than Sarah, Jane received half of what Lucy and Sarah got together, and Camille received CZK 500 less than Jane. How many CZK did each girl get?

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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