Sam needs 15 dozen gingerbread cookies. he bakes 2 dozen the first day, 4 dozens the next day, 6 dozens the day after that and this pattern continues. How many days does it take Sam to get his 15 gingerbread cookies if half of each batch gets eaten each night by his family and friends?
0: 2->1
1: 1+4=5->2.5
2: 2.5+6=8.5->4.25
3: 4.25+8=12.25->6.125
After n days, there are 2n + 1/(n+1)
On day n+1 there will be 2n + 1/(n+1) + 2(n+1)
So, we need 2n + 1/(n+1) + 2(n+1) >= 15
n > 3.2
A table of the days and dozens shows that he almost made it by day 3, and finally achieved 15 by day 4.
0: 2->1
1: 1+4=5->2.5
2: 2.5+6=8.5->4.25
3: 4.25+8=12.25->6.125
4: 6.25+10=16.25
the answer is 5 days because the family and friends eat only half of the gingerbread cookies each day
day 1: 2-1=1
day 2: 1+4=5-2=3
day 3: 3+6=9-3=6
day 4: 6+8=14-4=10
day 5: 10+10=20-5=15
You just need to keep adding the old gingerbread cookies with the new and each day he keeps doubling the batches.
To answer this question, we need to calculate the total number of gingerbread cookies baked by Sam each day and subtract the number eaten by his family and friends. Let's break down the problem step by step:
1. Calculate the number of gingerbread cookies baked each day by Sam:
- On the first day: 2 dozen gingerbread cookies = 2 x 12 = 24 cookies
- On the second day: 4 dozen gingerbread cookies = 4 x 12 = 48 cookies
- On the third day: 6 dozen gingerbread cookies = 6 x 12 = 72 cookies
2. Determine the number of cookies eaten each day:
- On the first day: half of the batch, so 24 / 2 = 12 cookies eaten.
- On the second day: half of the batch, so 48 / 2 = 24 cookies eaten.
- On the third day: half of the batch, so 72 / 2 = 36 cookies eaten.
3. Calculate the number of cookies remaining after each day:
- On the first day: 24 - 12 = 12 cookies remaining.
- On the second day: 48 - 24 = 24 cookies remaining.
- On the third day: 72 - 36 = 36 cookies remaining.
4. Continue this pattern until we have at least 15 gingerbread cookies remaining:
- On the fourth day: 8 dozen gingerbread cookies = 8 x 12 = 96 cookies, so after eating half, we have 96 / 2 = 48 cookies remaining.
- On the fifth day: 10 dozen gingerbread cookies = 10 x 12 = 120 cookies, so after eating half, we have 120 / 2 = 60 cookies remaining.
- On the sixth day: 12 dozen gingerbread cookies = 12 x 12 = 144 cookies, so after eating half, we have 144 / 2 = 72 cookies remaining.
5. As we can see, on the sixth day, Sam has 72 cookies remaining. This means he has reached his goal of 15 cookies, so it takes him 6 days to bake enough gingerbread cookies.
Therefore, it takes Sam 6 days to bake enough gingerbread cookies, following the given pattern and considering the half that gets eaten each night.