# Students

Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the rest of CZK 6,480. How many crowns did everyone receive?

A =  19440
B =  8100
C =  14580
D =  6480

### Step-by-step explanation:

A=2/5·(A+B+C+D)
B = 1/6·(A+B+C+D)
C = 3/10·(A+B+C+D)
D = 6480

3A-2B-2C-2D = 0
A-5B+C+D = 0
3A+3B-7C+3D = 0
D = 6480

Row 2 - 1/3 · Row 1 → Row 2
3A-2B-2C-2D = 0
-4.3333B+1.6667C+1.6667D = 0
3A+3B-7C+3D = 0
D = 6480

Row 3 - Row 1 → Row 3
3A-2B-2C-2D = 0
-4.3333B+1.6667C+1.6667D = 0
5B-5C+5D = 0
D = 6480

Pivot: Row 2 ↔ Row 3
3A-2B-2C-2D = 0
5B-5C+5D = 0
-4.3333B+1.6667C+1.6667D = 0
D = 6480

Row 3 - -4.33333333/5 · Row 2 → Row 3
3A-2B-2C-2D = 0
5B-5C+5D = 0
-2.6667C+6D = 0
D = 6480

D = 6480/1 = 6480
C = 0-6D/-2.66666667 = 0-6 · 6480/-2.66666667 = 14580
B = 0+5C-5D/5 = 0+5 · 14580-5 · 6480/5 = 8100
A = 0+2B+2C+2D/3 = 0+2 · 8100+2 · 14580+2 · 6480/3 = 19440

A = 19440
B = 8100
C = 14580
D = 6480

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