1. Four students, Amir, Boris, Tsvetko, and Darko, collected old paper. Together they collected $288 \mathrm{~kg}$ of paper. How many kilograms did each of them collect, given that Amir collected $36 \mathrm{~kg}$ more than Boris, which is $\frac{3}{4}$ of the amount collected together by Boris and Tsvetko, and Darko collected twice as much as Tsvetko?
Solution. Let $a, b, c, d$ denote the quantities of paper collected by the mentioned students. Then

$$
a=b+36, a=\frac{3}{4}(b+c), d=2 c, a+b+c+d=288
$$

From $b+36=\frac{3}{4}(b+c)$ we get $b=3 c-144$, then $a=3 c-108$ and if we substitute in $a+b+c+d=288$ we have

$$
(3 c-108)+(3 c-144)+c+2 c=288
$$

from which we find $c=60$, and then $b=36, a=72$ and $d=120$.