Kerri's father bill was a baker. Out of his usual morning batch of cookies bill burned the first 2 dozen cookies. He gave half of what was left to Keri to take to scol. He wrapped up half of the remaining cookies and have them to a group of fireman. He gave half of what was left to the policeman. If bill had only 7 cookies left, how many cookies were in the original batch?

2*7 = 14 before giving to cop

2*14 = 28 before giving to firemen
2*28=56 before giving to Keri
56+2*12 = 80 cookies to start with

start with 80
burned 24, leaving 56
Keri got 28, leaving 28
firemen got 14, leaving 14
cop got 7, leaving 7

7x2

14x2
28x2
56+12x2
80

Let's work through this step-by-step to find the number of cookies in the original batch.

1. Bill burned the first 2 dozen cookies:
Since 1 dozen is equal to 12, the first 2 dozen cookies burned would be 2 x 12 = 24 cookies.

2. Bill had (x - 24) cookies left after burning the first 2 dozen. (where x represents the original batch of cookies)

3. Bill gave half of what was left to Keri:
He gave (1/2)(x - 24) cookies to Keri.

4. Bill had (x - 24)/2 cookies left after giving half to Keri.

5. Bill wrapped up half of what was left and gave them to a group of firemen:
He gave [(1/2)((x - 24)/2)] cookies to the firemen.

6. Bill had [(x - 24)/2 - (1/2)((x - 24)/2)] cookies left after giving half to the firemen.

7. Bill gave half of what was left to the policeman:
He gave (1/2)[(x - 24)/2 - (1/2)((x - 24)/2)] cookies to the policeman.

8. Bill had (1/2)[(x - 24)/2 - (1/2)((x - 24)/2)] cookies left after giving half to the policeman.

9. The number of cookies left is given as 7, so we can set up the equation:
(1/2)[(x - 24)/2 - (1/2)((x - 24)/2)] = 7.

10. Solve the equation for x:
(1/2)[(x - 24)/2 - (1/2)((x - 24)/2)] = 7
[(x - 24)/2 - (1/2)((x - 24)/2)] = 14
[(x - 24)/2 - (x - 24)/4] = 14 (multiply both sides by 2)
[4(x - 24)/8 - (x - 24)/4] = 14
[4(x - 24) - 2(x - 24)]/8 = 14
[4x - 96 - 2x + 48]/8 = 14
[2x - 48]/8 = 14
2x - 48 = 8 * 14
2x - 48 = 112
2x = 112 + 48
2x = 160
x = 160/2
x = 80

Therefore, there were initially 80 cookies in the original batch.

To solve this problem, let's work backwards. We know that Bill had 7 cookies left, and before that, he gave half of what was left to the policeman.

Let's call the number of cookies after he gave half to the policeman as "x". Since half of "x" is equal to 7, we can set up the equation: (1/2) * x = 7.

To find "x", we can solve for it by multiplying both sides of the equation by 2: x = 14.

Now, before he gave half to the policeman, he wrapped up half of what was left for the firemen. So, let's call the number of cookies before he gave half to the policeman as "y". Since half of "y" is equal to "x" (which we found to be 14), we can set up the equation: (1/2) * y = 14.

Solving for "y", we can multiply both sides of the equation by 2: y = 28.

Now, before wrapping up half for the firemen, he gave half of what was left to Keri for school. Let's call the number of cookies before he gave half to Keri as "z". Since half of "z" is equal to "y" (which we found to be 28), we can set up the equation: (1/2) * z = 28.

Solving for "z", we can multiply both sides of the equation by 2: z = 56.

Finally, before he burned the first 2 dozen cookies, the original batch of cookies must have been larger than 56 cookies.

Since a dozen is equal to 12, two dozen cookies would be 2 * 12 = 24 cookies.

Therefore, the original batch of cookies must have been at least 56 + 24 = 80 cookies.