3. The father and mother have a total of 80 years. Their three children are 9, 7, and 2 years old. In a few years, the sum of the children's ages will be half the sum of the father's and mother's ages. How many years will the father be, and how many will the mother be, if the mother is six years younger than the father?
First solution.

Let $m$ be the number of mother's years. Then the number of father's years is $m+6$.

We have $m+m+6=80$.

1 POINT

By solving the equation, we get that the father is currently 43 years old, and the mother is 37 years old.

$1 \text{POINT}$

In $x$ years, the sum of the children's ages will be half the sum of the father's and mother's ages, so we have:

$(9+7+2)+3x=0.5(80+2x)$

2 POINTS

By solving the equation, we get $x=11$.

$1 \text{POINT}$

In 11 years, the father will be 54, and the mother will be 48 years old.

1 POINT

TOTAL 6 POINTS

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