Question

Помогите пж, срочно!Аня съела 1/3 всех конфет и ещё 2 конфеты, Маша съела 1/4 всех конфет и ещё 1 конфету, а Таня - половину тех конфет, которые остались после Ани и Маши. После этого осталось 1/6 часть первоначального числа конфет. Сколько конфет было в начале?

Answer 1

Х-всего кг.конфет. (1/3 *х+2)-съела Аня, (1/4*х+1)- съела Маша. получается что вместе Аня и Маша съели (7/12*х+3) конфет, следовательно после них осталось (5/12*х-3), тогда Таня съла 0,5*(5/12*х-3). Составим уравнение х- (1/3 *х+2)- (7/12*х+3)-0,5*(5/12*х-3)=1/6*х. Раскроем скобки и приведем подобные слагаемые получаем: х/24=3/2     х=(3*24)/2=36. Ответ 36кг конфет было первоначально

Answer 2

Problem Analysis

To solve this problem, we need to determine the initial number of candies based on the information given about the number of candies each person ate and the remaining fraction of candies.

Solution

Let's break down the information given step by step:

1. Ania ate 1/3 of all the candies and an additional 2 candies. 2. Masha ate 1/4 of all the candies and an additional 1 candy. 3. Tanya ate half of the remaining candies after Ania and Masha ate their share. 4. After all this, only 1/6 of the initial number of candies remained.

Let's assign variables to the unknowns: - Let x be the initial number of candies. - Let a be the number of candies Ania ate. - Let m be the number of candies Masha ate. - Let t be the number of candies Tanya ate.

Based on the given information, we can set up the following equations:

1. Ania ate 1/3 of all the candies and an additional 2 candies: - a = (1/3)x + 2

2. Masha ate 1/4 of all the candies and an additional 1 candy: - m = (1/4)x + 1

3. Tanya ate half of the remaining candies after Ania and Masha ate their share: - t = (1/2)(x - (a + m))

4. After all this, only 1/6 of the initial number of candies remained: - (1/6)x = x - (a + m + t)

Now, let's solve this system of equations to find the value of x, which represents the initial number of candies.

Solution Steps

1. Substitute the values of a and m from equations 1 and 2 into equation 3: - t = (1/2)(x - ((1/3)x + 2 + (1/4)x + 1))

2. Simplify equation 3: - t = (1/2)(x - (7/12)x - 3)) - t = (1/2)(5/12)x - 3/2

3. Substitute the value of t from equation 3 into equation 4: - (1/6)x = x - ((1/3)x + 2 + (1/4)x + 1 + (1/2)(5/12)x - 3/2))

4. Simplify equation 4: - (1/6)x = x - (7/12)x - 3 - (5/24)x + 3/2 - (1/6)x = (12/12)x - (7/12)x - (5/24)x + 3/2 - 3 - (1/6)x = (12/12 - 7/12 - 5/24)x + 3/2 - 3 - (1/6)x = (12 - 7 - 5/24)x + 3/2 - 3 - (1/6)x = (24/24 - 7 - 5/24)x + 3/2 - 3 - (1/6)x = (12/24 - 7 - 5/24)x + 3/2 - 3 - (1/6)x = (12 - 14 - 5/24)x + 3/2 - 3 - (1/6)x = (12 - 14 - 5/24)x + 3/2 - 6/2 - (1/6)x = (12 - 14 - 5/24)x - 3/2 - (1/6)x = (12 - 14 - 5/24)x - 3/2 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - (1/6)x = (288 - 336 - 70/24)x - 36/24 - **(1/6)x