5,6,7 |

Giuseppe has a sheet of plywood measuring $22 \times 15$. Giuseppe wants to cut as many rectangular blanks of size $3 \times 5$ as possible from it. How can he do this?
Note: more than 22 blanks cannot be obtained. Why?

## Solution

First, note that Giuseppe cannot obtain more blanks than $(22 \times 15) /(3 \times 5)=22$ pieces. Now let's proceed with the cutting.

![](https://cdn.mathpix.com/cropped/2024_05_06_34fd2032e75750f56a92g-11.jpg?height=166&width=274&top_left_y=1666&top_left_x=892)

Cut the sheet into three pieces along the 22 side: $5 \times 15$, $5 \times 15$, and $12 \times 15$. Now cut the third piece along the 12 side into four equal pieces $3 \times 15$. In total, you will get 6 pieces - two $5 \times 15$ and four $3 \times 15$. From the first two pieces, we will get 5 blanks $5 \times 3$ each, and from the remaining four pieces, we will get 3 blanks $3 \times 5$ each. In total, we will get 22 pieces (see the figure).

## Answer

See the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_34fd2032e75750f56a92g-11.jpg?height=186&width=288&top_left_y=2222&top_left_x=885)

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