Raskina I.V.

Once a trader came to the city with umbrellas of three colors. He had half as many blue umbrellas as yellow and red ones, red umbrellas were one-third the number of yellow and blue ones, and there were 45 yellow umbrellas. How many blue and how many red umbrellas did the trader have?
There are half as many blue umbrellas as yellow and red ones. This means that blue umbrellas make up a third of the total. Similarly, red umbrellas make up a quarter of the total. Let's draw a segment representing all the umbrellas. To conveniently represent both a third and a quarter of the entire segment, we will make it 12 cells long.

![](https://cdn.mathpix.com/cropped/2024_05_06_27dc4c83246cd1065e82g-10.jpg?height=91&width=918&top_left_y=789&top_left_x=570)

The segment for blue umbrellas is 4 cells long, the segment for red umbrellas is 3 cells long, and the segment for yellow umbrellas will be $12-3-4$ = 5 cells. If 45 umbrellas are represented by 5 cells, then each cell represents 9 umbrellas. Therefore, there are $4 \cdot 9=36$ blue umbrellas, and $3 \cdot 9=27$ red umbrellas.

## Answer

27 red and 36 blue.