# Three friends

Three friends divided the profit by 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.

a =  23400
b =  29250
c =  52000

### Step-by-step explanation:

104650 = a+b+c
5a = 4b
16b = 9c

104650 = a+b+c
5·a = 4·b
16·b = 9·c

a+b+c = 104650
5a-4b = 0
16b-9c = 0

Pivot: Row 1 ↔ Row 2
5a-4b = 0
a+b+c = 104650
16b-9c = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-4b = 0
1.8b+c = 104650
16b-9c = 0

Pivot: Row 2 ↔ Row 3
5a-4b = 0
16b-9c = 0
1.8b+c = 104650

Row 3 - 1.8/16 · Row 2 → Row 3
5a-4b = 0
16b-9c = 0
2.013c = 104650

c = 104650/2.0125 = 52000
b = 0+9c/16 = 0+9 · 52000/16 = 29250
a = 0+4b/5 = 0+4 · 29250/5 = 23400

a = 23400
b = 29250
c = 52000

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