Question 107968: Beth has hamsters at her house. The number of hamsters is equal to the sum of number of birds at Kristin's house and the number of dogs at Wendi's house. John has the same number of casts as Wendi has of dogs. If these four children have a total of 12 pets, how many pets are at each house?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! First of all, I will assume that there are at least one of each pet.
h=hampsters
b=birds
d=dogs
c=cats
Now we are told the following:
h=b+d-----------------eq1
c=d----------------------eq2
b+c+d+h=12----------------------eq3
Substitute eq1 and eq2 into eq3 and we get:
b+d+d+(b+d)=12 collect like terms
2b+3d=12 subtract 3d from both sides
2b=12-3d---------------------------------------eq3a
Now we have one equation in 2 unknowns but we can easily deal with it when we recognize a couple of things about pets.
1)----Pets cannot be negative!! Did you ever hear of a negative bird?
2)-----A third of a bird or a half a hampster???? Rediculous!!!
In other words, we are dealing in whole, positive numbers.
With this in mind, we can quickly look at eq3a and see that d must be < or = to 3. If d=4, then b=0 and that is at variance with our assumption; if d is > 4, then we start getting negative birds---No,No!! So lets look at the possibilities:
d=3-----------2b=12-9=3, b=1 1/2------------------No!!!!----half a bird
d=2------------2b=12-6=6, b=3----------------------bingo!!!!
d=1------------2b=13-3=9, b=4 1/2------------------No!!---half a bird, again
Now we have established that:
b=3
d=2---since c=d, then c=2
c=2
Substituting these into eq1, we get:
h=b+d=3+2=5
To sum everything up, we have:
birds=3
cats=2
dogs=2
hampsters=5
CK
hampsters=birds+dogs=3+2=5
5=5
cats=dogs
2=2
Hope this helps---ptaylor
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