# 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?

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

Our linear equations calculator calculates it.

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