How much does each animal weigh?

Question

Sue owns a pet store, she needs to fly some pets to a family in another town. She knows a small dog weighs 3 times as much as a cat. A parrot weighs half as much as a cat, and a rabbit weighs 2 pounds than a parrot. Sue is sending 2 dogs, 3 cats, 1 parrot, 4 rabbits to the family. How much does each animal weigh if the total weight is 130 pounds?

Answer 1

d = weight of dogs

c = weight of cats

p = weight of parrots

r = weight of rabbits

 

2 dogs, 3 cats, 1 parrot, 4 rabbits

Total weight of all animals is 130, so

2d + 3c + 1p + 4r = 130 (i)

 

Small dog weighs 3 times as much as a cat, so

d = 3c (ii)

 

Parrot weighs half as much as a cat, so

p = c/2 which is the same as

2p = c (iii)

 

Rabbit weighs 2 pounds less than a parrot, so

r = p - 2 (iv)

 

Let's try to get everything in terms of p.

 

Let's start by substituting equations (iii) into equation (ii)

d = 3c, c = 2p

d = 3(2p) = 6p (v)

 

Now substitute equations (v), (iii) and (iv) into equation (i)

 

2(6p) + 3(2p) + 1p + 4(p - 2) = 130

 

Solve for p

 

12p + 6p + 1p + 4p - 8 = 130

23p = 138

p = 6

 

So the number of parrots is 6

 

Using equation (iii), c = 2p = 2(6) = 12

 

So the number of cats is 12

 

Using equation (v), d = 6p = 6(6) = 36

 

So there are 36 dogs

 

Using equation (iv), r = p - 2 = 6 - 2 = 4

 

So the number of rabbits is 4