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?

Answer 1

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

Answer 2

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.