1. (10 points) On a tourist base, the number of two-room cottages is twice the number of one-room cottages. The number of three-room cottages is a multiple of the number of one-room cottages. If the number of three-room cottages is tripled, it will be 25 more than the number of two-room cottages. How many cottages are there in total on the tourist base, given that there are no fewer than 70?
Solution. Let the number of one-bedroom houses be $x$, two-bedroom houses $2 \mathrm{x}$, and three-bedroom houses nx.

$3 n x-25=2 x ; x(3 n-2)=25 ; \Rightarrow 25:(3 n-2) \Rightarrow 3 n-2=1 ; 5 ; 25$. If

$3 n-2=1 ; n=1 ; x=25 ; 25+50+25=100$ total houses.

If $3 n-2=5 ; 3 n=7$, which is impossible. If $3 n-2=25 ; 3 n=27 ; n=9 ; x=1 ; 1+2+9 is an insufficiently justified solution |
| 0 points | Incorrect reasoning or only the answer is written. |