## 172. Math Puzzle $9 / 79$

The Becker family from Halle has three children. They want to travel by train to visit relatives in Bitterfeld.

For Anja, this trip is still free of charge, as she is only two years old. Silke and Frank each have to pay half the adult fare. However, the family receives a one-third discount on the fare due to social policy measures for families with three or more children.

How much travel fare does the Becker family have to pay for the round trip (the full fare for one adult for the round trip is $4.80 \mathrm{M}$)?
Family Becker has to pay for four people. For two adults, the cost is: $2 \cdot 4.80 \mathrm{M}=9.60 \mathrm{M}$.

For two children, the cost is: $2 \cdot 2.40 \mathrm{M}=4.80 \mathrm{M}$.

This results in a total price of $9.60 \mathrm{M}+4.80 \mathrm{M}=14.40 \mathrm{M}$.

Since the family can travel at a third of the price, the total cost is 9.60 M; because:

$14.40 \mathrm{M}: 3=4.80 \mathrm{M} ; \quad 14.40 \mathrm{M}-4.80 \mathrm{M}=9.60 \mathrm{M}$.