Question

Если количество карандашей в коробке увеличить в 2 раза, то до полной коробки не хватит 3 карандаша. Если количество карандашей в коробке увеличить в 3 раза, то 7 карандашей не поместяться в коробке. Сколько карандашей в коробке? На сколько карандашей рассчитана коробка?

Answer 1

Problem Analysis

We are given two conditions: 1. If the number of pencils in the box is doubled, then there will be 3 pencils less than a full box. 2. If the number of pencils in the box is tripled, then 7 pencils will not fit in the box.

We need to determine the number of pencils in the box and the capacity of the box.

Solution

Let's assume the number of pencils in the box is x and the capacity of the box is c.

According to the first condition, if the number of pencils in the box is doubled, then there will be 3 pencils less than a full box. This can be represented as:

2x = c - 3

According to the second condition, if the number of pencils in the box is tripled, then 7 pencils will not fit in the box. This can be represented as:

3x > c + 7

We can solve these two equations to find the values of x and c.

Solving the Equations

Let's solve the equations using substitution:

From the first equation, we have:

2x = c - 3

Simplifying, we get:

c = 2x + 3

Substituting this value of c in the second equation, we have:

3x > (2x + 3) + 7

Simplifying further, we get:

x > 10

So, the number of pencils in the box is greater than 10.

Conclusion

Based on the given conditions, we can conclude that the number of pencils in the box is greater than 10. However, we cannot determine the exact number of pencils or the capacity of the box without additional information.

Please note that the search results provided by You.com did not provide any specific information related to this problem. Therefore, the solution is based on mathematical analysis and does not have a specific source citation.

If you have any further questions, feel free to ask!