Question

Петя и Вася принесли одинаковое количество N наборов плюшек к чаю. Каждый набор содержал либо 3, либо 5 плюшек. Когда каждый распаковал свои плюшки и выложил на тарелку, оказалось, что Петя принёс всего 25 плюшек, а Вася — 35. Найдите число N наборов, принесённых каждым из мальчиков.

Answer 1

3+3+3+3+3+5+5=25
5+5+5+5+5+5+5=35
Ответ: 7 наборов

Answer 2

Problem Analysis

- Петя и Вася принесли одинаковое количество N наборов плюшек к чаю. - Каждый набор содержал либо 3, либо 5 плюшек. - Петя принес 25 плюшек, а Вася - 35 плюшек. - Нужно найти число N наборов, принесенных каждым из мальчиков.

Solution

- Let's assume that Петя brought x sets of 3 plush toys and y sets of 5 plush toys. - Similarly, Вася brought a sets of 3 plush toys and b sets of 5 plush toys. - We can set up the following equations based on the given information: - Петя: 3x + 5y = 25 - Вася: 3a + 5b = 35 - We need to find the values of x and a, which represent the number of sets of 3 plush toys brought by Петя and Вася, respectively.

Solving the Equations

- We can solve the equations using the method of substitution or elimination. - Let's solve the equations using the method of substitution: - From the equation Петя: 3x + 5y = 25, we can rearrange it to get: y = (25 - 3x) / 5 - Substitute this value of y into the equation Вася: 3a + 5b = 35: - 3a + 5((25 - 3x) / 5) = 35 - Simplifying the equation, we get: 3a + 25 - 3x = 35 - Rearranging the equation, we get: 3a - 3x = 10 - Dividing the equation by 3, we get: a - x = 10/3 - Rearranging the equation, we get: a = x + 10/3 - Now, we have an equation for a in terms of x. We can substitute this value of a into the equation Петя: 3x + 5y = 25: - 3x + 5((25 - 3x) / 5) = 25 - Simplifying the equation, we get: 3x + 25 - 3x = 25 - The x terms cancel out, leaving us with: 25 = 25 - This equation is true for any value of x. Therefore, there are infinitely many solutions for this problem.

Conclusion

- The number of sets of plush toys brought by Петя and Вася cannot be determined uniquely based on the given information. - There are infinitely many possible combinations of x and a that satisfy the given conditions. - Therefore, we cannot find the exact value of N, the number of sets brought by each boy.