# Family

The family has four children. Ondra is three years older than Matthew, and Karlos 5 years older than the youngest Jane. We know that they have been together for 30 years, and three years ago, they were together for 19 years. Determine how old the children are.

O =  12
M =  9
K =  7
J =  2

### Step-by-step explanation:

O=3+M
K = 5+J
O+M+K+J=30
O-3+M-3+K-3=19

M-O = -3
J-K = -5
J+K+M+O = 30
K+M+O = 28

Pivot: Row 1 ↔ Row 2
J-K = -5
M-O = -3
J+K+M+O = 30
K+M+O = 28

Row 3 - Row 1 → Row 3
J-K = -5
M-O = -3
2K+M+O = 35
K+M+O = 28

Pivot: Row 2 ↔ Row 3
J-K = -5
2K+M+O = 35
M-O = -3
K+M+O = 28

Row 4 - 1/2 · Row 2 → Row 4
J-K = -5
2K+M+O = 35
M-O = -3
0.5M+0.5O = 10.5

Row 4 - 0.5 · Row 3 → Row 4
J-K = -5
2K+M+O = 35
M-O = -3
O = 12

O = 12/1 = 12
M = -3+O = -3+12 = 9
K = 35-M-O/2 = 35-9-12/2 = 7
J = -5+K = -5+7 = 2

J = 2
K = 7
M = 9
O = 12

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