Question

В пакете лежат конфеты. Если раздавать их детям по 5 конфет каждому, то не хватит 2 конфет, а если раздать по 4 конфеты, то в пакете еще останется 19 конфет. Сколько конфет в пакете?

Answer 1

Ответ:

составим систему

пусть количество детей будет х, а у - количеством конфет в пакете всего, тогда:

$y - 5x = - 2 \\ y - 4x = 19$

$y - 5x = - 2 \\ y = 19 + 4x$

подставим значение y в 1ое уравнение

$19 + 4x - 5x = - 2$

$- x = - 2 - 19$

$- x = - 21$

$x = 21$

подставим значение х во второе уравнение

$y = 19 + 4 \times 21$

$y = 19 + 84$

$y = 103$

Ответ:103конфеты

Answer 2

Problem Analysis

We are given that there are candies in a packet. If we distribute them to children, giving each child 5 candies, we will be 2 candies short. However, if we distribute them giving each child 4 candies, there will be 19 candies left in the packet. We need to determine the total number of candies in the packet.

Solution

Let's assume the total number of candies in the packet is x.

According to the given information: - If we distribute the candies to children, giving each child 5 candies, we will be 2 candies short. - If we distribute the candies to children, giving each child 4 candies, there will be 19 candies left in the packet.

Based on this information, we can set up the following equations:

Equation 1: x ÷ 5 - 2 = 0 (If we distribute the candies to children, giving each child 5 candies, we will be 2 candies short)

Equation 2: x ÷ 4 - 19 = 0 (If we distribute the candies to children, giving each child 4 candies, there will be 19 candies left in the packet)

To solve these equations, we can use algebraic methods.

Solving the Equations

Let's solve Equation 1 first:

x ÷ 5 - 2 = 0

Adding 2 to both sides of the equation:

x ÷ 5 = 2

Multiplying both sides of the equation by 5:

x = 10

So, the total number of candies in the packet is 10.

Now, let's solve Equation 2:

x ÷ 4 - 19 = 0

Adding 19 to both sides of the equation:

x ÷ 4 = 19

Multiplying both sides of the equation by 4:

x = 76

So, the total number of candies in the packet is 76.

Conclusion

Based on the given information, there are 10 candies in the packet.