Question

Мама купила трём своим детям 17 маленьких пирожных . Миша съел в два раза больше пирожных , чем Маша,а Даша съела больше Маши,но меньше Миши . Сколько пирожных съела Даша ?

Answer 1

Problem Analysis

We are given that a mother bought 17 small pastries for her three children. Misha ate twice as many pastries as Masha, and Dasha ate more than Masha but less than Misha. We need to determine how many pastries Dasha ate.

Solution

Let's assume that Masha ate x pastries. According to the given information, Misha ate twice as many pastries as Masha, so Misha ate 2x pastries. Dasha ate more than Masha but less than Misha, so Dasha ate between x and 2x pastries.

Since the total number of pastries is 17, we can write the equation:

x + 2x + (x < Dasha < 2x) = 17

Simplifying the equation:

4x < Dasha < 5x

Now, we need to find a value of x that satisfies the equation and ensures that Dasha's number of pastries is an integer.

Calculation

Let's try different values of x and check if they satisfy the equation:

- If x = 3, then 4x = 12 and 5x = 15. Since 12 < Dasha < 15, there is no integer value for Dasha that satisfies the equation. - If x = 4, then 4x = 16 and 5x = 20. Since 16 < Dasha < 20, there is no integer value for Dasha that satisfies the equation. - If x = 5, then 4x = 20 and 5x = 25. Since 20 < Dasha < 25, there is no integer value for Dasha that satisfies the equation. - If x = 6, then 4x = 24 and 5x = 30. Since 24 < Dasha < 30, there is no integer value for Dasha that satisfies the equation. - If x = 7, then 4x = 28 and 5x = 35. Since 28 < Dasha < 35, there is no integer value for Dasha that satisfies the equation. - If x = 8, then 4x = 32 and 5x = 40. Since 32 < Dasha < 40, there is no integer value for Dasha that satisfies the equation. - If x = 9, then 4x = 36 and 5x = 45. Since 36 < Dasha < 45, there is no integer value for Dasha that satisfies the equation. - If x = 10, then 4x = 40 and 5x = 50. Since 40 < Dasha < 50, there is no integer value for Dasha that satisfies the equation.

From the calculations, we can see that there is no integer value for x that satisfies the equation and ensures that Dasha's number of pastries is an integer. Therefore, it is not possible to determine how many pastries Dasha ate based on the given information.

Conclusion

Based on the given information, it is not possible to determine how many pastries Dasha ate.