Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3

of the remaining cookies, and when Carla came home, she ate 1/2
of the cookies on the plate. When their mother came home, there were 2 cookies on the plate. How many did each child eat?

total cookies = X.

Alex ate: 1/4 * x = x/4 cookies. Bal. = 3x/4.

Bernice ate: 1/3 * 3x/4 = 3x/12 = x/4 cookies. Bal. = x/2.

Carla ate: 1/2 * x/2 = x/4 cookies. Bal. = x/4.

x/4 = 2, X = 8 Cookies.
So each child ate x/4 or 2 cookies.

Well, it seems like those cookies went through quite the adventure! Let's break it down.

Alex devoured 1/4 of the cookies, leaving behind 3/4.
Then, Bernice came along and munchered 1/3 of the remaining cookies, leaving behind 2/3.
Next up was Carla, who gobbled up 1/2 of the cookies that were on the plate, leaving 2 cookies behind.

So, if we put all the clues together, we know that those 2 cookies represent 2/3 of what was originally on the plate.

To figure out how many cookies each child ate, we have to work our way backward. If 2/3 of the cookies were left, that means 1/3 of the original amount was eaten (since 1/3 + 2/3 = 1).

Now, if 1/3 of the cookies equates to 2, then we can multiply both sides by 3 to find out the original amount.

1/3 * 3 = 2 * 3
1 = 6

So, the original amount of cookies was 6.

Now let's take a look at how many each child ate!

Alex devoured 1/4 of the cookies, which is 1/4 * 6 = 1.5 cookies (but since we can't have half a cookie, we round down to 1).

Bernice came next and had 2/3 * 6 = 4 cookies to choose from. She ate 1/3 of those, which is 1/3 * 4 = 1.33 (but since we don't have a cookie cutting tool that delicate, we round down to 1 as well).

Lastly, Carla got the remaining 2 cookies and ate half, which is 2/2 = 1 cookie.

So to sum it up:
- Alex ate 1 cookie
- Bernice ate 1 cookie
- Carla ate 1 cookie

And together, they devoured the math problem and left me with the job of explaining it all to you. Bon appé!

Let's break down the steps to solve this problem:

1. Start with the total number of cookies on the plate.
2. Alex ate 1/4 of the cookies, so subtract 1/4 from the total.
3. Bernice then ate 1/3 of the remaining cookies, so subtract 1/3 from the previous result.
4. Finally, Carla ate 1/2 of the remaining cookies, so subtract 1/2 from the previous result.
5. The result should be equal to the 2 cookies left on the plate.

Let's calculate step by step:

1. Total number of cookies: x

2. Alex ate 1/4 of the cookies:
Remaining cookies = x - (1/4)x = (3/4)x

3. Bernice ate 1/3 of the remaining cookies:
Remaining cookies = (3/4)x - (1/3)(3/4)x = (9/12)x - (3/12)x = (6/12)x = (1/2)x

4. Carla ate 1/2 of the remaining cookies:
Remaining cookies = (1/2)x - (1/2)(1/2)x = (1/2)x - (1/4)x = (2/4)x - (1/4)x = (1/4)x

5. Finally, we know that the remaining cookies equal 2:
(1/4)x = 2

To find the value of x, we can multiply both sides of the equation by 4:
x = 8

Now we can substitute this value back into the previous steps to find out how many cookies each child ate:

- Alex ate 1/4 of 8 cookies = (1/4) * 8 = 2 cookies.
- Bernice ate 1/3 of the remaining 6 cookies = (1/3) * 6 = 2 cookies.
- Carla ate 1/2 of the remaining 4 cookies = (1/2) * 4 = 2 cookies.

Therefore, each child ate 2 cookies.

To find out how many cookies each child ate, we need to work backwards from the information provided. Let's break it down step by step:

1. Let's assume that the total number of cookies on the plate is represented by "C."

2. According to the given information, Alex ate 1/4 of the cookies. So, the number of cookies remaining after Alex ate can be calculated by subtracting 1/4 of C from C:
Remaining after Alex = C - (1/4)C = (3/4)C.

3. Bernice then ate 1/3 of the remaining cookies. So, the number of cookies remaining after Bernice ate can be calculated by subtracting 1/3 of (3/4)C from (3/4)C:
Remaining after Bernice = (3/4)C - (1/3)(3/4)C = (2/3)(3/4)C = (2/4)C = (1/2)C.

4. Carla then ate 1/2 of the remaining cookies. So, the number of cookies remaining after Carla ate can be calculated by subtracting 1/2 of (1/2)C from (1/2)C:
Remaining after Carla = (1/2)C - (1/2)(1/2)C = (1/2)C - (1/4)C = (2/4)C - (1/4)C = (1/4)C.

5. The problem states that when their mother came home, there were 2 cookies on the plate. Therefore, we can set up an equation:
Remaining after Carla = (1/4)C = 2.

6. Now, we can solve the equation to find the value of C, which represents the total number of cookies initially on the plate:
(1/4)C = 2.
Multiplying both sides of the equation by (4/1) to get rid of the fraction:
4 * (1/4)C = 4 * 2.
C = 8.

Therefore, the total number of cookies initially on the plate (C) is 8.

Now, let's calculate how many cookies each child ate:

1. Alex ate 1/4 of the cookies, which is (1/4) * 8 = 2 cookies.
2. Bernice ate 1/3 of the remaining cookies, which is (1/3) * (3/4) * 8 = 2 cookies.
3. Carla ate 1/2 of the remaining cookies, which is (1/2) * (1/2) * 8 = 2 cookies.

So, Alex ate 2 cookies, Bernice ate 2 cookies, and Carla ate 2 cookies.