Question 61333: Hi there, I am hoping you can help me help my daughter. She has a multiple step word problem that goes like this: What will be the total number of rats from January 1 to January 1 the next year? The following assumtions are to be made for solving this problem. 1. Original pair of rats are one female and one male. 2. The number of young produced in every litter is six, and three of those six are females. 3. The original female gives birth to six young on Jan. 1 and produces another litter of six 40 days later and every 40 days thereafter as long as she lives. 4. Each female born will produce her first litter 120 days after her birth, and then produce a new ltter every 40 days therafter. 5. The rats are on an island with no natural enemies and plenty of food. Therefore, in this first year, there are only births, and no rats die.
This assignment was adapted from Mathematics Insight and Meaning, Jan de Lange, The Netherlands, 1987. Thank you in advance for you help. Lisa
Answer by 303795(602)   (Show Source):
You can put this solution on YOUR website! For this problem if the first litter is born on the Ist of January and every 40 days thereafter then there will be 10 sets of birth dates in total.
To solve the problem I drew up a table with 10 rows (1 for each of the birth dates) and 4 columns(with headings Breeders, Breed next Set, Breed in Two sets and Breed in three sets). The table also had an extra column and row for the necessary headings and labels.
Set 1
There are the 2 original breeders and 6 who will be able to breed in three sets time.
Set 2
There are the 2 original breeders, 6 who will be able to breed in two sets time and 6 who will breed in three sets time.
Set 3
There are the 2 original breeders, 6 who will breed next set, 6 who will be able to breed in two sets time and 6 who will breed in three sets time.
Set 4
There are now 8 breeders, 6 who will breed next set, 6 who will be able to breed in two sets time and 24 who will breed in three sets time.
Set 5
There are now 14 breeders, 6 who will breed next set, 24 who will be able to breed in two sets time and 42 who will breed in three sets time.
Set 6
There are now 20 breeders, 24 who will breed next set, 42 who will be able to breed in two sets time and 60 who will breed in three sets time.
Set 7
There are now 44 breeders, 42 who will breed next set, 60 who will be able to breed in two sets time and 132 who will breed in three sets time.
Set 8
There are now 86 breeders, 60 who will breed next set, 132 who will be able to breed in two sets time and 258 who will breed in three sets time.
Set 9
There are now 146 breeders, 132 who will breed next set, 258 who will be able to breed in two sets time and 438 who will breed in three sets time.
Set 10
There are now 278 breeders, 258 who will breed next set, 438 who will be able to breed in two sets time and 834 who will breed in three sets time.
This is a total of 1808 rats.
(This is an ideal problem to model using a spreadsheet)
|
|
|
