Question

1. Мать поделила между сыновьями груши. Первому выдала половину всех груш и еще половину груши, второму- половину оставшегося и еще половину груши, а третьему- половину того, что осталось и еще половину груши. Ни одной груши при этом не нужно было разрезать. Сколько груш получил каждый сын, если мать раздала все груши?

Answer 1

Всего было 7 груш
первому дала половину груш и полгруши 3.5+0.5=4
Осталось три груши от этого числа дала половину груш и половину груши 1.5+0.5=2
осталось одна груша от этого числа дала половину груш и половину грушт 0.5+0.5=1
Итого было 7 дала 4, 2, 1

Answer 2

Problem Analysis

In this problem, a mother divided a certain number of pears among her three sons. The first son received half of all the pears and an additional half of a pear. The second son received half of the remaining pears and an additional half of a pear. The third son received half of the remaining pears and an additional half of a pear. We need to determine how many pears each son received.

Solution

Let's assume that the total number of pears the mother had was x.

The first son received half of all the pears, which is x/2, and an additional half of a pear, which is 1/2. So, the first son received x/2 + 1/2 pears.

The second son received half of the remaining pears after the first son's share, which is (x - (x/2 + 1/2))/2, and an additional half of a pear, which is 1/2. So, the second son received (x - (x/2 + 1/2))/2 + 1/2 pears.

The third son received half of the remaining pears after the second son's share, which is (x - (x/2 + 1/2) - ((x - (x/2 + 1/2))/2 + 1/2))/2, and an additional half of a pear, which is 1/2. So, the third son received (x - (x/2 + 1/2) - ((x - (x/2 + 1/2))/2 + 1/2))/2 + 1/2 pears.

To find the value of x, we can set up an equation using the information given in the problem:

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

Simplifying the equation:

x = x/2 + 1/2 + x/4 - x/4 + 1/4 + x/8 - x/8 + 1/8

Combining like terms:

x = x/2 + x/4 + x/8 + 1/2 + 1/4 + 1/8

Finding a common denominator:

x = (4x + 2x + x)/8 + (4 + 2 + 1)/8

Simplifying further:

x = 7x/8 + 7/8

Multiplying both sides by 8 to eliminate the denominator:

8x = 7x + 7

Subtracting 7x from both sides:

x = 7

Therefore, the mother had a total of 7 pears.

Now, we can substitute this value of x into the expressions we derived earlier to find out how many pears each son received.

The first son received x/2 + 1/2 = 7/2 + 1/2 = 4 pears.

The second son received (x - (x/2 + 1/2))/2 + 1/2 = (7 - (7/2 + 1/2))/2 + 1/2 = 2 pears.

The third son received (x - (x/2 + 1/2) - ((x - (x/2 + 1/2))/2 + 1/2))/2 + 1/2 = (7 - (7/2 + 1/2) - ((7 - (7/2 + 1/2))/2 + 1/2))/2 + 1/2 = 1 pear.

Therefore, the first son received 4 pears, the second son received 2 pears, and the third son received 1 pear.

Answer

The first son received 4 pears, the second son received 2 pears, and the third son received 1 pear.