# Together 4596

Pavel has half as much savings as Standa but the same savings as Radek. Standa saved CZK 120 less than Radek.

What savings do all three boys have together?

A) less than CZK 600
B) CZK 600
C) CZK 960
D) 1200 CZK
E) another number of crowns

x =  960 Kc

## Step-by-step explanation:

x=p+s+r
p=1.5 s
p=r
s = r-120

x=p+s+r
p=1.5·s
p=r
s = r-120

p+r+s-x = 0
p-1.5s = 0
p-r = 0
r-s = 120

Row 2 - Row 1 → Row 2
p+r+s-x = 0
-r-2.5s+x = 0
p-r = 0
r-s = 120

Row 3 - Row 1 → Row 3
p+r+s-x = 0
-r-2.5s+x = 0
-2r-s+x = 0
r-s = 120

Pivot: Row 2 ↔ Row 3
p+r+s-x = 0
-2r-s+x = 0
-r-2.5s+x = 0
r-s = 120

Row 3 - -1/-2 · Row 2 → Row 3
p+r+s-x = 0
-2r-s+x = 0
-2s+0.5x = 0
r-s = 120

Row 4 - 1/-2 · Row 2 → Row 4
p+r+s-x = 0
-2r-s+x = 0
-2s+0.5x = 0
-1.5s+0.5x = 120

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

x = 120/0.125 = 960
s = 0-0.5x/-2 = 0-0.5 · 960/-2 = 240
r = 0+s-x/-2 = 0+240-960/-2 = 360
p = 0-r-s+x = 0-360-240+960 = 360

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

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