1. A group of girls and boys collected 1700 denars for their friend's birthday gift. The girls contributed 200 denars each, and the boys contributed 300 denars each. How many girls and how many boys were there, if the group had an odd number of members.
Solution. Let $d$ be the number of girls and $m$ be the number of boys. We have

$$
300 m+200 d=170 S \text { i.e. } 3 d+2 m=17
$$

Then we get $2 d=17-3 m$. $m$ can take values from 1 to 5, and since $2 d$ is even, $m$ can be 1, 3, and 5. If $m=1, d=7, m+d=8$; if $m=3, d=4, m+d=7$; if $m=5, d=1, m+d=6$. Since $m+d$ is odd, we get that the number of boys is 3 and the number of girls is 4.