Friends 5

Erik is friends with two girls, Markéta and Lenka, and two boys, Tomáš and Robo. When his mother wanted to know how old these children are, he told her a riddle: Tomáš is two years older than Robo. The sum of the boys' ages is the same as the sum of the girls' ages. Markéta is twice as old as Lenka. A year ago, Tomáš had twice as much as Lenka had then. How old are the children?

Final Answer:

t =  7
l =  4
r =  5
m =  8

Step-by-step explanation:

$$\begin{gathered} t=2+r \\ t+r=m+l \\ m=2l \\ t-1=2(l-1) \\ t+(t-2)=(2l)+l \\ t-1=2(l-1) \\ t+(t-2)=(2\cdot l)+l \\ t-1=2\cdot (l-1) \\ 3l-2t=-2 \\ 2l-t=1 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 0.33t=2.33 \\ t=\frac{2.33333333}{0.33333333}=7 \\ l=\frac{-2+2t}{3}=\frac{-2+2\cdot 7}{3}=4 \\ l=4 \\ t=7 \end{gathered}$$

$r=t-2=7-2=5$

$m=2\cdot l=2\cdot 4=8$

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