At the Pet Store - Part Two

Probability Level pending

At the Pets R Us pet store, they only have guinea pigs, parrots, cats and fish. All the pets are parrots, except 20 of them. All the pets are cats, except 21 of them. All the pets are guinea pigs, except 25 of them. All the pets are fish, except 18 of them.

Q1. How many pets does Pets R Us have?

Q2. If Adam wants to buy a cat, how many options does he have?

Note: If your answer is 15 for Q1, and 4 for Q2, type in the SUM OF THE TWO NUMBERS, so 15 + 4 = 19. That's what you have to type.

Copyright for image - Emil Boczek.


The answer is 35.

Pola Forest by Pola Forest , 21, United Kingdom

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4 solutions

Let parrot be denoted by a, guinea pig by b, cats by c, and fish by d so the equations now formed are:
b+c+d=20
a+b+d=21
a+c+d=25
a+b+c=18
solve the four equations to get four unknowns
a=8 ; b=3 ; c=7 ; d=10
so, total no. of pets= 28
and no. of choice in cats= 7


2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ryan Redz
Jun 2, 2014

If there are 20 animals that are not parrots, then there are a total of 20 guinea pigs, cats, and fish. Therefore guinea pigs (g) + cats (c) + fish (fish)=20 this follows that: g + c + f = 20 g + p (parrots) + f = 21 p + c + f = 25 g + p + c = 18 Use any algebraic methods in solving 4 variables. in my case I use RREF p=8, c=7,g=3,f=10, total 28 + 7(fish) = 35

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Anirudh Krishna
May 7, 2014

Let the total no.of pets be 'x' No.of guinea pigs = x-25 (given) No.of parrots = x-20 (given) No.of cats = x-21 (given) No.of fishes = x-18 (given)

Now, total no. of pets = x = x-25 + x-20 + x-21 + x-18 x = 4x-84 -3x = -84 x = 28 From this we could get, no.of cats = x-21 = 28-21 = 7 Therefore the required answer is 28+7 = 35

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Alan Hu
Apr 29, 2014

Since there are 20 animals that are not parrots, we see that that there are a total of 20 guinea pigs, cats, and fish.

Therefore guinea pigs ( g ) + cats ( c ) + fish ( fish )=20

Applying this logic, we get four equations, and four variables.

g + c + f = 20

g + p (parrots) + f = 21

p + c + f = 25

g + p + c = 18

Adding all of these equations together we have:

3( g + p + c + f ) = 84

Dividing by 3 shows us that the total number of animals is 28.

Since g + p + c + f = 28 and g + p + f = 21, we subtract the second equation from the first to find that the number of cats is 7.

28 + 7 = 35, which is our answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

let x x be the total numbers of pets

p a r r o t s = x − 20 parrots = x -20

c a t s = x − 21 cats = x - 21

g u i n e a p i g s = x − 25 guinea pigs = x - 25

f i s h = x − 18 fish = x - 18

t o t a l = p a r r o t s + c a t s + g u i n e a p i g s + f i s h total = parrots + cats + guinea pigs + fish

substitute the above values

x = ( x − 20 ) + ( x − 21 ) + ( x − 25 ) + ( x − 18 ) x = (x - 20) + (x -21) + (x-25) + (x-18)

x = 28 ; c a t s = 7 x = 28 ; cats = 7

28 + 7 = 35 28 + 7 = \boxed{35}

Unstable Chickoy - 7 years ago

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