5.3. Nadya 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 Nadya bake?
Answer: 21 raspberry pies, 7 blueberry pies, and 14 strawberry pies.

Solution. First method. Since the number of raspberry pies is half of the total, the number of blueberry and strawberry pies together is the same as the number of raspberry pies (see Fig. 5.3). Moreover, there are 14 fewer blueberry pies than raspberry pies, so these 14 pies are strawberry pies. Therefore, the number of raspberry and blueberry pies: \(14 \cdot 2 = 28\), which means a total of \(28 + 14 = 42\) pies were baked. 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_3ededfe9bc358e4d64a4g-1.jpg?height=264&width=975&top_left_y=2030&top_left_x=597)

Fig. 5.3

Second method. Let \(x\) be the number of raspberry pies. Then the total number of pies baked is \(2x\), of which \(x - 14\) are blueberry pies, so the number of strawberry pies is \(2x - x - (x - 14) = 14\). Knowing that the number of strawberry pies is half the number of raspberry and blueberry pies together, we set up the equation: \(x + x - 14 = 2 \cdot 14\), from which \(x = 21\).

Thus, there are 21 raspberry pies, and the number of blueberry pies is \(21 - 14 = 7\).

## Grading Criteria:

+ Correct answer and correct solution provided

\(\pm\) Correct and justified reasoning provided, but one arithmetic error

\(\pm\) The number of pies of only one type or the total number of pies is correctly found, but the complete answer is not obtained

\(\mp\) The equation is correctly set up, but not solved

干 Correct answer provided, verified that it satisfies the condition, but not proven that other answers are impossible

- Only the answer is provided