Question

ПОМОГИТЕ ПОЖАЛУЙСТА РЕШИТЬ ЗАДАЧКУ!!! Бабушка поставила перед тремя внуками вазочку с шоколадными батончиками.За угощением внуки подходили поочерёдно.Первый по просьбе бабушки взял 1/4 всех батончиков и ещё один батончиков.Второму было предложено взять 1/4 того что осталось и ещё 2 батончика.третьему пологалось взять также 1/4 остатка и ещё 3 батончика.После чего ваза опустела.Докажи что всем внукам досталось поровну.

Answer 1

Х, шт - общее количество шоколадных батонов

тогда

1-й внук взял:

а=х*1/4+1

значит осталось:

в=х-а

2-й внук взял:

с=в*1/4+2

значит осталось:

д=в-с

3-й внук взял:

е=д*1/4+3

и всего осталось = 0

тогда (постепенно избавляемся от всех переменных, расписываю по шагам, что бы было понятно)

х-а-с-е=0

х-(х*1/4+1)-(в*1/4+2)-(д*1/4+3)=0

х-х*1/4-1-((х-х*1/4+1)*1/4+2)-((в-с)*1/4+3)=0

х-х*1/4-1-х*1/4+х*1/16-1/4-2-((в-с)*1/4+3)=0

х-х*1/2+х*1/16-13/4-(в-с)*1/4-3=0

х-х*1/2+х*1/16-13/4-((х-а-в*1/4+2)*1/4-3=0

х-х*1/2+х*1/16-13/4-((х-х*1/4-1-х+х*1/4+1)*1/4+2)*1/4-3=0

х-х*1/2+х*1/16-13/4-1/2-3=0

х*(1-1/2+1/16)=13/4+1/2+3

х*9/16=27/4

х=(27/4)/(9/16)

х=12

12*1/4+1=3+1=4 - досталось первому внуку

(12-4)*1/4+2=2+2=4 - досталось второму внуку

(12-4-4)*1/4+3=1+3=4 - досталось третьему внуку

Ответ: каждому из внуков досталось по 4 шоколадных батона

Answer 2

Х-всего батончиков
1) 1/4*х+1
2) (х-1/4*х-1)*1/4 +2=3/16*х +7/4
поровну, значит:
3/16*х +7/4=1/4*х+1
х=12

Answer 3

Problem Analysis

In this problem, we need to prove that all three grandchildren received an equal number of chocolate bars from their grandmother. The problem provides us with the following information: - The grandmother placed a bowl of chocolate bars in front of the three grandchildren. - The first grandchild took 1/4 of all the bars and an additional one bar. - The second grandchild took 1/4 of what was left and an additional two bars. - The third grandchild was supposed to take 1/4 of the remaining bars and an additional three bars. - After this, the bowl was empty.

To prove that all three grandchildren received an equal number of chocolate bars, we need to show that the amount taken by each grandchild is the same.

Solution

Let's assume that the total number of chocolate bars in the bowl is represented by the variable x.

According to the problem, the first grandchild took 1/4 of all the bars and an additional one bar. This can be represented as: - First grandchild: (1/4)x + 1

The second grandchild took 1/4 of what was left after the first grandchild took their share, and an additional two bars. This can be represented as: - Second grandchild: (1/4)(x - (1/4)x - 1) + 2

The third grandchild was supposed to take 1/4 of the remaining bars after the second grandchild took their share, and an additional three bars. This can be represented as: - Third grandchild: (1/4)(x - (1/4)(x - (1/4)x - 1) - 2) + 3

According to the problem, the bowl was empty after the third grandchild took their share. Therefore, we can set up the following equation: - (1/4)(x - (1/4)(x - (1/4)x - 1) - 2) + 3 = 0

To prove that all three grandchildren received an equal number of chocolate bars, we need to show that this equation has a solution where x is a whole number.

Solving the Equation

Let's solve the equation step by step:

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

Simplifying the equation:

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

Multiplying both sides of the equation by 4 to eliminate the fraction:

x - (1/4)(x - (1/4)x - 1) - 2 = -12

Expanding the equation:

x - (1/4)(x - (1/4)x - 1) - 2 = -12 x - (1/4)(x - (1/4)x) - (1/4)(-1) - 2 = -12 x - (1/4)(x - (1/4)x) + (1/4) - 2 = -12 x - (1/4)x + (1/16)x + (1/4) + (1/4) - 2 = -12 (15/16)x + 1/2 = -12

Subtracting 1/2 from both sides of the equation:

(15/16)x = -12 - 1/2 (15/