[Text problems (other)]

Nadia baked pies with raspberries, blueberries, and strawberries. The number of pies with raspberries was half of the total number of pies; the number of pies with blueberries was 14 less than the number of pies with raspberries. And the number of pies with strawberries was half the number of pies with raspberries and blueberries combined. How many pies of each kind did Nadia bake?

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Since the number of raspberry pies is half of the total number, the number of blueberry and strawberry pies together is the same as the number of raspberry pies (see the diagram). At the same time, there are 14 fewer blueberry pies than raspberry pies, so these 14 pies are strawberry pies. Then the number of raspberry and blueberry pies: $14 \cdot 2=28$, so the total number of pies baked is $28+14=42$. Thus, the number of raspberry pies is $42: 2=21$, blueberry pies - 7, and strawberry pies - 14.

![](https://cdn.mathpix.com/cropped/2024_05_06_79aa1f75de69bad6c7b2g-03.jpg?height=323&width=1132&top_left_y=2371&top_left_x=454)

## Answer

21 raspberry pies, 7 blueberry pies, and 14 strawberry pies.

Postman Pechkin delivers mail by bicycle to four villages: Prostokvashino, Smetanino, Tvorozhnoye, and Molochnoye (see the diagram). He knows that the distance from Prostokvashino to Tvorozhnoye is 9 km, from Prostokvashino to Smetanino is 13 km, from Tvorozhnoye to Smetanino is 8 km, and from Tvorozhnoye to Molochnoye is 14 km. Find the distance from Prostokvashino to Molochnoye.

![](https://cdn.mathpix.com/cropped/2024_05_06_79aa1f75de69bad6c7b2g-04.jpg?height=463&width=829&top_left_y=332&top_left_x=612)

## Solution

The distance from Prostokvashino to Smetanino via Tvorozhnoye is $9+8=17$ (km), while the direct distance is 13 km. Therefore, the detour to Tvorozhnoye (to and from the highway) is 4 km. The distance from Prostokvashino to Molochnoye via Tvorozhnoye is $9+14=23$ (km), and without the detour: $23-4=19$ (km).

## Answer

19 km.