5.1. Evgeny is tiling the floor of his living room, which measures 12 by 16 meters. He plans to place 1 m $\times$ 1 m square tiles along the perimeter of the room, and the rest of the floor will be covered with 2 m $\times$ 2 m square tiles. How many tiles will he need in total?
Solution. Let's step back 1 meter from the living room's boundaries. We will be left with a rectangle of size $10 \times 14$, which needs to be covered with $2 \times 2$ tiles. The area of the rectangle is 140, and the area of one tile is 4, so we will need $140: 4=35$ large tiles. The area of the boundary strip is $12 \cdot 16-140=52$ and it needs to be covered with tiles of area 1. Therefore, 52 small tiles will be required. The total number of tiles is $35+52=87$.

Answer. 87 tiles.