Question

Карандаши разделили на 2 неравные кучки. Когда из первой переложили половину имевшихся в ней карандашей во вторую кучку, а затем из второй кучки переложили в первую половину карандашей, оказавшихся во второй, то в первой стало 18 карандашей, а во второй 8 карандашей. Сколько карандашей было в каждой кучке первоначально?

Answer 1

Будем идти с конца:
В первой: Во второй:
18. 8.
Если из второй переложили в первую, то было 8•2 во второй
10. 16.
С этим действием аналогично.
20. 6.

Answer 2

Problem Analysis

We are given that a number of pencils were divided into two unequal piles. Half of the pencils from the first pile were transferred to the second pile, and then half of the pencils from the second pile were transferred back to the first pile. After these transfers, there were 18 pencils in the first pile and 8 pencils in the second pile. We need to determine the initial number of pencils in each pile.

Solution

Let's assume that the initial number of pencils in the first pile is x and the initial number of pencils in the second pile is y.

According to the given information, we can set up the following equations:

1. After transferring half of the pencils from the first pile to the second pile, the number of pencils in the first pile becomes x/2 and the number of pencils in the second pile becomes y + (x/2).

2. After transferring half of the pencils from the second pile back to the first pile, the number of pencils in the first pile becomes (x/2) + (y/2) and the number of pencils in the second pile becomes (y + (x/2)) - (y/2).

We are also given that after these transfers, there were 18 pencils in the first pile and 8 pencils in the second pile. So we can set up the following equations:

3. (x/2) + (y/2) = 18 4. (y + (x/2)) - (y/2) = 8

Let's solve these equations to find the values of x and y.

Solution Steps

Step 1: Simplify equation 4: - (y + (x/2)) - (y/2) = 8 - (y + x/2) - y/2 = 8 - y + x/2 - y/2 = 8 - x/2 - y/2 = 8 - (x - y)/2 = 8 - x - y = 16

Step 2: Substitute the value of (x - y) from equation 3 into equation 4: - x - y = 16 - x = 16 + y

Step 3: Substitute the value of x from step 2 into equation 3: - (x/2) + (y/2) = 18 - ((16 + y)/2) + (y/2) = 18 - (16 + y + y)/2 = 18 - (16 + 2y)/2 = 18 - 16 + 2y = 36 - 2y = 36 - 16 - 2y = 20 - y = 20/2 - y = 10

Step 4: Substitute the value of y from step 3 into equation 2 to find x: - x = 16 + y - x = 16 + 10 - x = 26

Answer

Therefore, the initial number of pencils in the first pile was 26 and the initial number of pencils in the second pile was 10.

Please let me know if I can help you with anything else.