The Animals in Shadowbrook Forest

Algebra Level 3

Shadowbrook forest is populated with 25 animals. Out of these animals, there are seven different species. The seven species are mouse , rabbit , squirrel , duck , deer , fox , and bear . There are more mice than there are rabbits, and there are more squirrels than rabbits, and also more squirrels than mice. The duck, mice, and fox populations are equal, and there are three more deer than bears. There are also two more deer than foxes. There is one bear in Shadowbrook forest.

The next day, two fox cubs are born. The male fox goes hunting to provide for his mate and their cubs, and catches two squirrels. The bear, meanwhile, catches a duck.

What is $\frac { { \text{squirrel} }_{ \text{pop}. }-{ \text{duck} }_{\text{pop}. } }{ { \text{mouse} }_{ \text{pop}. } }$ now?

Details and Assumptions :

Animal populations are whole numbers
There cannot be 0 or negative numbers of animals

None of these choices 5.5 4.5 5 3

2 solutions

Justine Allen Arciga
Apr 24, 2015

Bear = 1

Deers = 3 + bear = 4

Foxes = deeers - 2 = 2

Foxes = ducks = mice = 2

Mice > rabbits... 2 > 1 (nonzero and nonnegative)

Rabbit = 1

Squirrels > mice > rabbits

Total no of animals is 25

Squirrels = 25 - bear - deers - foxes - ducks - mice - rabbit = 25 - 1 - 4 - 2 - 2 - 2 - 1

Squirrels = 13

Next day: Foxes = 2 + 2 = 4 (not needed to get the answer)

Squirrel = 13 - 2 = 11

Ducks = 2 - 1 = 1

11 squirrels minus 1 duck is 10, then divide it by 2 mice. The answer is 5.

It helps in visualisation by drawing model.

Julian Poon - 6 years, 1 month ago

Yes, it does. Visuals are always essential to fully understanding a problem, in my opinion. c:

Maddie Anderson - 6 years, 1 month ago

Maddie Anderson
Apr 22, 2015

First, we have to find the initial animal populations.

$squirrels > mice > rabbits$ , $ducks = mice = foxes$ , $deer = foxes + 2$ , and $deer = bears +3$ . Since there's only one bear, we can plug that into the last equation and work backwards to find that $deer = 4$ and $foxes = 2$ , which means that $ducks$ and $mice$ also equal 2.

There are more $mice$ than $rabbits$ , and our population numbers must be positive whole numbers, so $rabbits$ has to equal 1.

If we add all of these numbers up, we get 12. There are 25 animals in the forest, and the only ones we haven't counted are the squirrels, so there must be $25 - 12$ or 13 squirrels.

The next day, two fox cubs are born, so now $foxes = 4$ . The male fox catches two squirrels, cutting the squirrel population down to 11. The bear also catches a duck, and now only one duck remains. 11 squirrels minus one duck equals 10, and that number divided by the mice, which remains 2, equals 5. There's our answer!

I think this problem can have an even more interesting name....😁

Arnav Das - 5 years, 8 months ago

The Animals in Shadowbrook Forest

2 solutions

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