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 school. He wrapped up half of the remaining cookies and have them to a group of fireman. He gave two thirds of what was left to the policeman. If bill had only 7 cookies left, how many cookies were in the original batch?
7×3/2×2×2+24 is your answer.
You just go backwards. For example, instead of 1/2 you would flip it and do times 2.
Am I making sense or do you need me to explain more?
It makes sense thank you!
[(x-24)/2 ] after Keri
[(x-24)/4 ] after firemen
[(x-24)/4 ] (1/3) after policeman
= 7
so
[(x-24)/4 ] = 21
(x-24) = 84
x = 108
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check
(108 - 24 /4 = 21
* 1/3 = 7 sure enough
Idk 66?
To solve this problem, we can work backwards to determine the original number of cookies in the batch. Let's go step by step:
1. We know that Bill had 7 cookies left at the end.
2. Before giving cookies to the policeman, Bill must have had more cookies.
3. Let's say he had X number of cookies before giving some to the policeman.
4. Bill gave two-thirds of what was left to the policemen, so he must have had (2/3)X cookies after giving some to the policemen.
5. Before giving cookies to the policemen, Bill must have had more cookies.
6. Let's say he had Y number of cookies before giving some to the firefighters.
7. Bill wrapped up half of the remaining cookies and gave them to a group of firefighters, so he must have had (1/2)Y cookies after giving some to the firefighters.
8. Before giving cookies to the firefighters, Bill must have had more cookies.
9. Let's say he had Z number of cookies before giving some to Keri.
10. Bill gave half of what was left to Keri, so he must have had (1/2)Z cookies after giving some to Keri.
11. Before giving cookies to Keri, Bill must have had more cookies.
12. Let's say he had A number of cookies in the original batch.
Now, using the information we have, we can put together the following equation:
(1/2)Z = (1/2)Y + 2 [After giving cookies to Keri]
(1/2)Y = (2/3)X + 5 [After giving cookies to firefighters]
(2/3)X = A + 7 [After giving cookies to policemen]
Now we can solve the equations step by step to find the value of A, which represents the original number of cookies in the batch.
From equation 1:
(1/2)Z - (1/2)Y = 2
From equation 2:
(1/2)Y - (2/3)X = 5
Combining equations 1 and 2, we get:
(1/2)Z - (2/3)X = 7
From equation 3:
(2/3)X - A = 7
Now, let's express A in terms of Z:
(2/3)X - (2/3)X + (1/2)Z - (2/3)X = 7
(1/2)Z - (2/3)X = 7
(1/2)Z = 7
Z = 14
Therefore, the original number of cookies in the batch was 14.