Strange Animals - Part 2
Algebra
Level
2
All except 2 of my pets are dogs.
All except 2 of my pets are cats.
All except 2 of my pets are birds.
All except 2 of my pets are crocodiles.
How many pets do I have?
4
3
Statements cannot be satisfied.
2
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Let me have a dogs, b cats, c birds, d crocodiles and e other pets. Each of these variables is a non-negative integer. We are given that ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ b + c + d + e = 2 , a + c + d + e = 2 , a + b + d + e = 2 , a + b + c + e = 2 .
Subtracting the first 2 equations, we get that a = b . Similarly, the other equations give us a = b = c = d . Hence, we have to solve 3 a + e = 2 .
Since a and e are non-negative integers, the only solution is a = 0 , e = 2 . Thus, I have a + b + c + d + e = 4 a + e = 2 pets in total.