Combined savings

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

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

Final Answer:

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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