One afternoon Mr. and Mrs. Baxter and their 3 children were busy working outside in their garden. Mrs. Baxter was feeling hungry, so she went inside to the kitchen where there was a plate full of cookies. She ate 1/6 of the cookies and then went back to work. Mr. Baxter was feeling hungry, so he went inside and ate 1/5 of the remaining cookies and then went back to work. Next, Anna was feeling hungry, so she went inside and ate 1/4 of the cookies that were left on the plate and then went back to work. Then Tyler was feeling hungry, so he went inside, ate 1/3 of the cookies left on the plate and then went back to work. Finally, little Adam was feeling hungry, and he went inside and ate 1/2 of the remaining cookies, leaving 4 cookies on the plate. How many cookies were on the plate before anyone started feeling hungry?

Question

One afternoon Mr. and Mrs. Baxter and their 3 children were busy working outside in their garden. Mrs. Baxter was feeling hungry, so she went inside to the kitchen where there was a plate full of cookies. She ate 1/6 of the cookies and then went back to work. Mr. Baxter was feeling hungry, so he went inside and ate 1/5 of the remaining cookies and then went back to work. Next, Anna was feeling hungry, so she went inside and ate 1/4 of the cookies that were left on the plate and then went back to work. Then Tyler was feeling hungry, so he went inside, ate 1/3 of the cookies left on the plate and then went back to work. Finally, little Adam was feeling hungry, and he went inside and ate 1/2 of the remaining cookies, leaving 4 cookies on the plate. How many cookies were on the plate before anyone started feeling hungry?

Answer 1

think of it like this

eating 1/6 leaves 5/6
eating 1/5 of that leaves 4/6
...
so, 1/6 of the cookies was 4.

Answer 2

Let's work through this step-by-step:

Step 1: Mrs. Baxter eats 1/6 of the cookies on the plate.
If there were C cookies on the plate initially, she eats (1/6) * C cookies.

Step 2: Mr. Baxter eats 1/5 of the remaining cookies on the plate.
After Step 1, there are (1 - 1/6) * C cookies left on the plate.
Mr. Baxter eats (1/5) * [(1 - 1/6) * C] cookies.

Step 3: Anna eats 1/4 of the remaining cookies on the plate.
After Step 2, there are (1 - 1/5) * [(1 - 1/6) * C] cookies left on the plate.
Anna eats (1/4) * [(1 - 1/5) * [(1 - 1/6) * C]] cookies.

Step 4: Tyler eats 1/3 of the remaining cookies on the plate.
After Step 3, there are (1 - 1/4) * [(1 - 1/5) * [(1 - 1/6) * C]] cookies left on the plate.
Tyler eats (1/3) * [(1 - 1/4) * [(1 - 1/5) * [(1 - 1/6) * C]]] cookies.

Step 5: Adam eats 1/2 of the remaining cookies on the plate, leaving 4 cookies.
After Step 4, there are (1 - 1/3) * [(1 - 1/4) * [(1 - 1/5) * [(1 - 1/6) * C]]] cookies left on the plate.
Adam eats (1/2) * [(1 - 1/3) * [(1 - 1/4) * [(1 - 1/5) * [(1 - 1/6) * C]]]] cookies.

Step 6: Set up an equation using the information from Step 5.
The equation becomes: (1/2) * [(1 - 1/3) * [(1 - 1/4) * [(1 - 1/5) * [(1 - 1/6) * C]]]] = 4.

Step 7: Solve the equation from Step 6 to find the value of C.
Simplify the equation and solve for C.

C = (2 * 3 * 4 * 5 * 6 * 4) / [(2 * 3) + (3 * 4) + (4 * 5) + (5 * 6) + (6 * 4)].

C = 720 / (6 + 12 + 20 + 30 + 24).

C = 720 / 92.

C ≈ 7.83.

Therefore, there were approximately 7.83 cookies on the plate before anyone started feeling hungry.

Answer 3

To find out how many cookies were on the plate before anyone started feeling hungry, we can work backwards.

Let's start with the information given: Little Adam ate 1/2 of the remaining cookies and left 4 cookies on the plate.

If 4 cookies are 1/2 of the remaining cookies, that means the remaining cookies must have originally been 2 times the number of cookies left (since 2 is the reciprocal of 1/2).

So, let's set up an equation: 2 * remaining cookies = total number of cookies.

Now, we can go through each step backwards using the information given for each family member.

Tyler ate 1/3 of the cookies that were left. This means 2/3 of the cookies remained. So, we can say 2/3 * remaining cookies = total number of cookies.

Anna ate 1/4 of the cookies that were left. This means 3/4 of the cookies remained. So, we can say 3/4 * remaining cookies = total number of cookies.

Mr. Baxter ate 1/5 of the remaining cookies. This means 4/5 of the cookies remained. So, we can say 4/5 * remaining cookies = total number of cookies.

Mrs. Baxter ate 1/6 of the cookies. This means 5/6 of the cookies remained. So, we can say 5/6 * remaining cookies = total number of cookies.

Now, we need to solve the equation to find the remaining cookies:

(5/6) * (4/5) * (3/4) * (2/3) * remaining cookies = total number of cookies.

Simplifying the equation:

(5/6) * (4/5) * (3/4) * (2/3) * remaining cookies = total number of cookies
(1/6) * remaining cookies = total number of cookies

Dividing both sides of the equation by (1/6):

remaining cookies = total number of cookies * 6.

Since we're looking for the total number of cookies, we want to isolate it. Dividing both sides of the equation by 6:

total number of cookies = remaining cookies / 6.

Substituting the value of remaining cookies from the given information (remaining cookies = 4):

total number of cookies = 4 / 6 = 2/3.

Therefore, there were 2/3 of a cookie on the plate before anyone started feeling hungry.