Question

Мама купила несколько груш. Старшему отдала половину всех груш и еще одну грушу. Среднему – половину оставшихся груш и еще две груши. Младшему – половину оставшихся груш и еще три груши. Сколько груш купила мама, если груш не осталось.

Answer 1

Ответ:

Всего было 34 груши.

Пошаговое объяснение:

решаем без составления уравнения. Начинаем с конца:

младший получил "половину оставшихся и еще три " (три последние по условию).

Замечание: на каждом этапе деления число груш было четное, иначе пополам разделить их не удалось бы.

Пробуем.

От некоторого числа Х (остаток после раздачи старшему и среднему) отняли его половину, и получили число 3:

X-X/2=3; X/2=3; X=6.

Вот. Младший получил 6. А средний? А средний получил (6+2)*2=16. А старший получил (16+1)*2=34. Значит всего было 34 (груши).

Проверяем:

старшему: 34:2+1=18; осталось 34-18=16

среднему: 16:2+2=10; осталось 16-10=6

младшему: 6:2+3=6 не осталось ничего!

Все верно.

Answer 2

Problem Analysis

The problem states that a mother bought several pears and distributed them among her three children. The oldest child received half of all the pears plus one more pear. The middle child received half of the remaining pears plus two more pears. The youngest child received half of the remaining pears plus three more pears. We need to determine how many pears the mother bought if there are no pears left.

Solution

Let's solve the problem step by step.

1. Let's assume the number of pears the mother bought is x.

2. The oldest child received half of all the pears plus one more pear. So, the oldest child received (x/2) + 1 pears.

3. The middle child received half of the remaining pears plus two more pears. After the oldest child took their share, there are x - ((x/2) + 1) pears left. The middle child received half of these remaining pears plus two more pears. So, the middle child received ((x - ((x/2) + 1))/2) + 2 pears.

4. The youngest child received half of the remaining pears plus three more pears. After the middle child took their share, there are (x - ((x/2) + 1)) - (((x - ((x/2) + 1))/2) + 2) pears left. The youngest child received half of these remaining pears plus three more pears. So, the youngest child received (((x - ((x/2) + 1)) - (((x - ((x/2) + 1))/2) + 2))/2) + 3 pears.

5. According to the problem, there are no pears left. So, the expression for the youngest child's share should be equal to zero: (((x - ((x/2) + 1)) - (((x - ((x/2) + 1))/2) + 2))/2) + 3 = 0

6. Now, we can solve the equation to find the value of x, which represents the number of pears the mother bought.

Calculation

Let's solve the equation to find the value of x.

(((x - ((x/2) + 1)) - (((x - ((x/2) + 1))/2) + 2))/2) + 3 = 0

Simplifying the equation:

(((x - (x/2) - 1)) - (((x - (x/2) - 1)/2) + 2))/2) + 3 = 0

(((x - x/2 - 1)) - (((x - x/2 - 1)/2) + 2))/2) + 3 = 0

(((2x/2 - x/2 - 1)) - (((2x/2 - x/2 - 1)/2) + 2))/2) + 3 = 0

(((x/2 - 1)) - (((x/2 - 1)/2) + 2))/2) + 3 = 0

(((x/2 - 1)) - ((x/4 - 1/2) + 2))/2) + 3 = 0

(((x/2 - 1)) - (x/4 - 1/2 + 2))/2) + 3 = 0

(((x/2 - 1)) - (x/4 + 3/2))/2) + 3 = 0

(((x/2 - 1)) - (x/4 + 3/2))/2) + 3 = 0

(((x/2 - 1)) - (x/4 + 3/2))/2) + 3 = 0

((2(x/2 - 1)) - (x/4 + 3/2))/2) + 3 = 0

((2x/2 - 2) - (x/4 + 3/2))/2) + 3 = 0

((x - 2) - (x/4 + 3/2))/2) + 3 = 0

((x - 2) - (x/4 + 3/2))/2) + 3 = 0

((4(x - 2)) - (x + 6))/8) + 3 = 0

((4x - 8) - (x + 6))/8) + 3 = 0

((4x - 8 - x - 6))/8) + 3 = 0

((3x - 14))/8) + 3 = 0

3x - 14 + 24 = 0

3x + 10 = 0

3x = -10

x = -10/3

The solution to the equation is x = -10/3.

However, since the number of pears cannot be negative or fractional, we can conclude that there is no valid solution to this problem. It seems there is an error or inconsistency in the problem statement.

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