B3. The ages of three cousins, Mark, Gregor, and Denis, are in the ratio 2:4:7. Together, they are 65 years old.

a) How old is each of them?

b) In how many years will Denis be twice as old as Mark?

c) How old were Gregor and Denis when Mark was born?
B3. We consider the age ratio. Marko's age is denoted by $2 x$, Gregor's by $4 x$, and Denis's by $7 x$. We write the equation $2 x+4 x+7 x=65$, from which $x=5$. Marko is 10 years old, Gregor is 20 years old, and Denis is 35 years old.

Suppose that in $y$ years, Denis will be twice as old as Marko: $35+y=2(10+y)$. From this, we get $y=15$. In 15 years, Denis will be twice as old as Marko.

Marko was born 10 years ago. At that time, Gregor was 10 years old, and Denis was 25 years old.

Scoring: Total: 7 points

![](https://cdn.mathpix.com/cropped/2024_06_07_e4711ece0d44ad9bc5c3g-7.jpg?height=60&width=1605&top_left_y=2546&top_left_x=311)

![](https://cdn.mathpix.com/cropped/2024_06_07_e4711ece0d44ad9bc5c3g-7.jpg?height=46&width=1545&top_left_y=2601&top_left_x=370)

Answer, e.g.: Marko is 10 years old, Gregor is 20 years old, and Denis is 35 years old. ................ 1 p
b) Equation written: $(10+x) \cdot 2=35+x$ ..... 1 p
Solution to the equation: $x=15$ ..... 1 p
Answer, e.g.: In 15 years, Denis will be twice as old as Marko. ..... 1 p
c) Gregor was 10 years old, and Denis was 25 years old. ..... 1 p