## Task 2 - 300712

Five students from class 7a collected waste paper. Of the total amount they collected together, Marco contributed a quarter, Frank a sixth, Matthias a fifth, and Steffen a tenth. Dirk collected $2 \mathrm{~kg}$ more than Marco.

a) How many kilograms of waste paper did each of these five students contribute?

b) What amount was paid for the total amount of paper delivered by the five students, if 30 Pfennig were paid for each kilogram?
If the five students collected a total of $x$ kilograms of waste paper, then Marco contributed $\frac{x}{4}$, Falk $\frac{x}{6}$, Matthias $\frac{x}{5}$, Steffen $\frac{x}{10}$, and Dirk $\frac{x}{4}+2$ kilograms. Therefore, we have

$$
x=\frac{x}{4}+\frac{x}{6}+\frac{x}{5}+\frac{x}{10}+\frac{x}{4}+2=\frac{58 x}{60}+2 \quad \Rightarrow \quad x=60
$$

a) Therefore, Marco contributed $15 \mathrm{~kg}$, Falk $10 \mathrm{~kg}$, Matthias $12 \mathrm{~kg}$, Steffen $6 \mathrm{~kg}$, and Dirk $17 \mathrm{~kg}$.

b) Since $60 \cdot 30=1800$, the collected waste paper was paid $18 \mathrm{M}$.