# Together 20433

Pavel received half as much money from his parents as Petr and Milan and half as much as Pavel. How much did all the boys get together? The parents gave Milan CZK 1,350.

x =  2850

## Step-by-step explanation:

x=A+P+M
A = P + P/2
M = A + A/2
M=1350

A+M+P-x = 0
2A-3P = 0
3A-2M = 0
M = 1350

Pivot: Row 1 ↔ Row 3
3A-2M = 0
2A-3P = 0
A+M+P-x = 0
M = 1350

Row 2 - 2/3 · Row 1 → Row 2
3A-2M = 0
1.3333M-3P = 0
A+M+P-x = 0
M = 1350

Row 3 - 1/3 · Row 1 → Row 3
3A-2M = 0
1.3333M-3P = 0
1.6667M+P-x = 0
M = 1350

Pivot: Row 2 ↔ Row 3
3A-2M = 0
1.6667M+P-x = 0
1.3333M-3P = 0
M = 1350

Row 3 - 1.33333333/1.66666667 · Row 2 → Row 3
3A-2M = 0
1.6667M+P-x = 0
-3.8P+0.8x = 0
M = 1350

Row 4 - 1/1.66666667 · Row 2 → Row 4
3A-2M = 0
1.6667M+P-x = 0
-3.8P+0.8x = 0
-0.6P+0.6x = 1350

Row 4 - -0.6/-3.8 · Row 3 → Row 4
3A-2M = 0
1.6667M+P-x = 0
-3.8P+0.8x = 0
0.4737x = 1350

x = 1350/0.47368421 = 2850
P = 0-0.8x/-3.8 = 0-0.8 · 2850/-3.8 = 600
M = 0-P+x/1.66666667 = 0-600+2850/1.66666667 = 1350
A = 0+2M/3 = 0+2 · 1350/3 = 900

A = 900
M = 1350
P = 600
x = 2850

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