# Distributed 7694

The children have 568 cards distributed as follows: Jano and Mišo in the ratio of 3:7 and Mišo and Laco in the ratio of 3:5. How many cards does Mišo have?

m =  183.5077

## Step-by-step explanation:

j+m+l = 568
j = 3/7 · m
m = 3/5 · l

j+l+m = 568
7j-3m = 0
3l-5m = 0

Pivot: Row 1 ↔ Row 2
7j-3m = 0
j+l+m = 568
3l-5m = 0

Row 2 - 1/7 · Row 1 → Row 2
7j-3m = 0
l+1.429m = 568
3l-5m = 0

Pivot: Row 2 ↔ Row 3
7j-3m = 0
3l-5m = 0
l+1.429m = 568

Row 3 - 1/3 · Row 2 → Row 3
7j-3m = 0
3l-5m = 0
3.095m = 568

m = 568/3.0952381 = 183.50769231
l = 0+5m/3 = 0+5 · 183.50769231/3 = 305.84615385
j = 0+3m/7 = 0+3 · 183.50769231/7 = 78.64615385

j = 5112/65 ≈ 78.646154
l = 3976/13 ≈ 305.846154
m = 11928/65 ≈ 183.507692

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