Together 6187

Petr had 20% more savings than Jana, who saved half of what Markéta did. Together they saved CZK 2,520. How much CZK did each of them save?

Correct answer:

j =  600
m =  1200
p =  720

Step-by-step explanation:


p=1.20·j
j = m/2
2520 = p+m+j

1.2j-p = 0
2j-m = 0
j+m+p = 2520

Pivot: Row 1 ↔ Row 2
2j-m = 0
1.2j-p = 0
j+m+p = 2520

Row 2 - 1.2/2 · Row 1 → Row 2
2j-m = 0
0.6m-p = 0
j+m+p = 2520

Row 3 - 1/2 · Row 1 → Row 3
2j-m = 0
0.6m-p = 0
1.5m+p = 2520

Pivot: Row 2 ↔ Row 3
2j-m = 0
1.5m+p = 2520
0.6m-p = 0

Row 3 - 0.6/1.5 · Row 2 → Row 3
2j-m = 0
1.5m+p = 2520
-1.4p = -1008


p = -1008/-1.4 = 720
m = 2520-p/1.5 = 2520-720/1.5 = 1200
j = 0+m/2 = 0+1200/2 = 600

j = 600
m = 1200
p = 720

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