Savings

Paul has by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have three boys together?

Correct answer:

x =  960 Kc

Step-by-step explanation:


p=s+s/2
p=r
s = r-120
x=p+s+r

2p-3s = 0
p-r = 0
r-s = 120
p+r+s-x = 0

Row 2 - 1/2 · Row 1 → Row 2
2p-3s = 0
-r+1.5s = 0
r-s = 120
p+r+s-x = 0

Row 4 - 1/2 · Row 1 → Row 4
2p-3s = 0
-r+1.5s = 0
r-s = 120
r+2.5s-x = 0

Row 3 + Row 2 → Row 3
2p-3s = 0
-r+1.5s = 0
0.5s = 120
r+2.5s-x = 0

Row 4 + Row 2 → Row 4
2p-3s = 0
-r+1.5s = 0
0.5s = 120
4s-x = 0

Pivot: Row 3 ↔ Row 4
2p-3s = 0
-r+1.5s = 0
4s-x = 0
0.5s = 120

Row 4 - 0.5/4 · Row 3 → Row 4
2p-3s = 0
-r+1.5s = 0
4s-x = 0
0.125x = 120


x = 120/0.125 = 960
s = 0+x/4 = 0+960/4 = 240
r = 0-1.5s/-1 = 0-1.5 · 240/-1 = 360
p = 0+3s/2 = 0+3 · 240/2 = 360

p = 360
r = 360
s = 240
x = 960

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