A word problem?

Question

My word problem deals with the population explosion of cats.
Here it is:
If a mother cat has 4 kittens every 6 months and two are male and 2 are female, how many cats will there be in two years ?
The rules:
All months are 30 days long.
Pregnancy lasts 60 days.
All female cats become pregnant when they are six months old.
All animals live.
Bonus:
How many litters does each generation have?

Answer 1

It sort of depends on when the clock starts ticking. Is "month 0" right when the mother cat has the first litter, or is it the start of the 6-month cycle?

If the latter:
The original mother cat will have 4 kittens @6 months, 4 @12 months, 4 @18 months, and 4 @2 years. 17 cats so far (mother + 16 kittens)

The 2 second-generation females born @6 months will get pregnant @12 months and have litters @14 and @20 months. 16 more kittens (2*2*4), total 33.

The 2 second-generation females @12 months will get pregnant @18 months and have litters @20 months. 8 more kittens, total 41.

The second-generation females @18 months and later don't have time to get pregnant AND have a litter by the 24th month.

The 4 third-generation females born @14 months will get pregnant @20 months and have 16 kittens @22 months. 16 more kittens, total 57.

None of the other third-generation females, or any of the fourth-generation females, will have time to get pregnant before the 2 years runs out.

The mother cat has 4 litters.
The 2 second-generation females born @6 months have 2 litters, @12 months have 1 litter, and @18/24 months do not give birth. The second generation has 6 litters.
The 4 third-generation females born @14 months have 1 litter. The third-generation has 4 litters.

14 total litters (4 for the 1st generation, 6 for the 2nd, 4 for the 3rd) @ 4 kittens each, is 56 kittens. Add in the original mother cat, for 57.

Answer 2

eliminate the fact that says "pregnancy lasts 60 days"

2 years = 24 months

the mother cat can be pregnant every 6 months, so she can only be pregnent 4 times in two years.

every time she gets pregnant she have 2 male cat and 2 female cat. Total of 4 cats

so in 2 years she can produces 16 cats consist of 8 females and 8 males.

Starting from the 6th month, that's when the 8 cats become 6 months old. Since there are only 18 months left, the 8 females cats can be pregnant only 3 times. One of them can produces 12 cats. Since there 8 of them, together, the produces 96 cats Consist of 48 males and 48 females

Now start from 12th month. That's when the 48 female cat's become pregnant. THey con only be pregnant 2 times. 1 cat can produce 8 cats. 48 cats can produce 384 cats consist of 192 males and 192 females

Now start from 18months. That's when the 192 famale cats become pregnant. They can only be pregnant once. One cat produces 6 cats. 192 cats produce 1152 cats.

The total will be 1 + 16 + 96 + 384 + 1152 = 1649 cats in two years. (include the first mom)


and i'm totally NOT sure of my answer. LOL

Answer 3

Assuming she starts at 6 months old into 2 years. 2 years is 365 * 2 =730 days - (6 * 30) =550. 550/60 =9.1666 births. 1 birth = 4 kittens.
9.166 * 4 = 36.666 kittens in 2 years or 6 months after age of maturity.
How many litters does each generation have ?
36.66/2 =18.333 females * 36.666 kittens within 550 days = 672.197 kittens/4 =168.04 litters.

Answer 4

Number of starting cats and if cats were pregnant to begin with was not mentioned or how long.
c+cat, M=tom, F=Female, p=Pregnant cat
m1: 5c_2m3f, 1p
m3: 5c_2m3f, 2p
m7: 9c_4m5f, 1p
m9: 17c_8m9f, 2p
m11: 17c_8m9f, 6p
m13: 21c_10m13f, 1p
ETC, too HARD!
18,704 That is a _LOT_ Oops forgot mom, 18705