Question

141 конфету разложили по 10 пакетам для новогодних подарков. Известно, что в некоторых пакетах лежит по 12 конфет, а в каждом из остальных конфет также поровну. Пете на Новый Год подарили такой пакет. Сколько конфет ему могло достаться?​

Answer 1

Ответ:

14 конфет могло достаться Пете

Пошаговое объяснение:

141÷10

Answer 2

Problem Analysis

We are given that 141 candies are divided into 10 packets for New Year's gifts. Some packets contain 12 candies each, while the remaining packets have an equal number of candies. We need to determine how many candies Pete could have received.

Solution

To solve this problem, we can use a simple equation. Let's assume that the number of packets with an equal number of candies is x. Since there are 10 packets in total, the number of packets with 12 candies each will be (10 - x).

The total number of candies can be calculated by multiplying the number of packets with 12 candies by 12 and adding the product of the number of packets with an equal number of candies (x) and the number of candies in each packet.

We can set up the following equation to represent the given information:

12 * (10 - x) + x * (number of candies in each packet) = total number of candies

We know that the total number of candies is 141. Let's substitute this value into the equation and solve for x.

Calculation

12 * (10 - x) + x * (number of candies in each packet) = 141

Simplifying the equation:

120 - 12x + x * (number of candies in each packet) = 141

Rearranging the equation:

x * (number of candies in each packet) - 12x = 141 - 120

x * (number of candies in each packet - 12) = 21

Dividing both sides of the equation by (number of candies in each packet - 12):

x = 21 / (number of candies in each packet - 12)

Now, we need to find the value of (number of candies in each packet) that satisfies the equation. We can do this by trying different values and checking if the result is an integer.

Calculation Continued

Let's try different values for (number of candies in each packet) and see if we get an integer value for x:

For (number of candies in each packet) = 13: x = 21 / (13 - 12) = 21 / 1 = 21

For (number of candies in each packet) = 14: x = 21 / (14 - 12) = 21 / 2 = 10.5 (not an integer)

For (number of candies in each packet) = 15: x = 21 / (15 - 12) = 21 / 3 = 7

For (number of candies in each packet) = 16: x = 21 / (16 - 12) = 21 / 4 = 5.25 (not an integer)

For (number of candies in each packet) = 17: x = 21 / (17 - 12) = 21 / 5 = 4.2 (not an integer)

For (number of candies in each packet) = 18: x = 21 / (18 - 12) = 21 / 6 = 3.5 (not an integer)

For (number of candies in each packet) = 19: x = 21 / (19 - 12) = 21 / 7 = 3

For (number of candies in each packet) = 20: x = 21 / (20 - 12) = 21 / 8 = 2.625 (not an integer)

For (number of candies in each packet) = 21: x = 21 / (21 - 12) = 21 / 9 = 2.333 (not an integer)

For (number of candies in each packet) = 22: x = 21 / (22 - 12) = 21 / 10 = 2.1 (not an integer)

For (number of candies in each packet) = 23: x = 21 / (23 - 12) = 21 / 11 = 1.909 (not an integer)

For (number of candies in each packet) = 24: x = 21 / (24 - 12) = 21 / 12 = 1.75 (not an integer)

From the calculations above, we can see that the only value of (number of candies in each packet) that gives an integer value for x is 13.

Therefore, if each packet contains 13 candies, Pete could have received 21 candies.

Answer

Pete could have received 21 candies.